Monitoring path design device, monitoring path design method, and program

Abstract

A monitoring path designing device according to an aspect of the present disclosure, which is to design a monitoring path for estimating the state of a target network, has an objective function creating unit configured to use an undirected graph representative of the topology of the target network, thereby creating an objective function representative of the effectiveness of the monitoring path in a format that enables a calculation using an Ising machine.

Description

Technical Field

[0001] The present disclosure relates to a monitoring path design apparatus, a monitoring path design method, and a program.

Background Art

[0002] In order to stably operate a network system, it is important to estimate various states (such as delay and failure) of the target network. For this reason, in recent years, in addition to passive monitoring that collects logs, metrics, etc. from NW devices, active monitoring is also often performed. Active monitoring is a monitoring method that performs end-to-end measurement on the target network using ping or the like and estimates the state from measurement values such as connectivity and RTT (Round-Trip Time). A technique for estimating the state of the target network by such end-to-end measurement is also called network tomography and has been actively studied.

[0003] In network tomography, not only the method for estimating the network state (Non-Patent Document 1) but also how to design a highly effective monitoring path for estimating the network state is important. In fact, a method has been proposed in which, after defining an objective function representing the effectiveness of the monitoring path, a path design that maximizes it is searched (Non-Patent Document 2).

[0004] In network tomography, consider the problem of designing a highly effective monitoring path for estimating the binary states representing the normality or abnormality of nodes and links on a network. In network tomography, end-to-end measurements are performed between multiple remote nodes. At this time, the path through which test packets pass is called a monitoring path. It is desirable to design the monitoring path in advance from the viewpoints of cost, ease of operation, etc. Also, since network states (variations in failure locations) are diverse, a monitoring path that can distinguish various states is considered excellent. However, when the network scale is large, it is mathematically difficult to design an optimal monitoring path. In Non-Patent Document 2, the effectiveness of the monitoring path is defined by a function called distinguishability, and an attempt is made to maximize it using an algorithm based on the greedy method, but this method can only reach an approximate optimal solution.

[0005] On the other hand, in recent years, a computer called a quantum computer has been known (Non-Patent Documents 3 and 4), and many computational examples showing higher performance than classical computers have been reported. A quantum computer can solve combinatorial optimization problems expressed in the form of HOBO (Higher Order Binary Optimization) or QUBO (Higher Order Binary Optimization). Note that a general methodology for reducing the order of HOBO to QUBO is also known (Non-Patent Document 5).

Prior Art Documents

Non-Patent Documents

[0006]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Non-Patent Document 4

Non-Patent Document 5

Summary of the Invention

Problems to be Solved by the Invention

[0007] If the problem of maximizing distinguishability indicating the effectiveness of the monitoring path can be formulated in the form of HOBO or QUBO, it is considered that a more effective monitoring path can be obtained as the optimal solution by the Ising machine.

[0008] The present disclosure has been made in view of the above points, and provides a technique for designing an effective monitoring path.

Means for Solving the Problems

[0009] A monitoring path design device according to an aspect of the present disclosure is a monitoring path design device that designs a monitoring path for estimating the state of a target network, and is configured to create, in a form computable by an Ising machine, an objective function representing the effectiveness of the monitoring path using an undirected graph representing the topology of the target network, and includes an objective function creation unit.

Advantages of the Invention

[0010] A technique for designing a highly effective monitoring path is provided.

Brief Description of the Drawings

[0011]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Modes for Carrying Out the Invention

[0012] Hereinafter, an embodiment of the present invention will be described. In the following embodiments, a method of formulating the problem of maximizing distinguishability, which indicates the effectiveness of a monitoring path, into the HOBO or QUBO form is proposed. Further, a monitoring path design device 10 capable of designing a highly effective monitoring path using an Ising machine will be described according to this proposed method.

[0013] <Proposed Method> First, the proposed method will be described.

[0014] <<Positioning of the annealing machine and the proposed method>> The proposed method provides a formulation method for executing calculations on an annealing machine. Therefore, first, the annealing machine will be briefly described to clarify the positioning of the proposed method.

[0015] First, the Ising model, which is the basis of the annealing machine, will be described. The Ising model is a mathematical model originally proposed to explain the thermal behavior of magnetic materials and has its origin in statistical mechanics. The Hamiltonian function H representing the energy of the system (this function is also called the Ising Hamiltonian or simply the Hamiltonian) is given by the following equation (1).

[0016]

Equation

[0017] In the case of a normal Ising model, spins are arranged in a lattice of arbitrary dimensions, interactions occur only between nearest-neighbor spins, and the magnetic field is uniform for all spins (that is, the magnetic field coefficient H i does not depend on i) is often considered. However, here, the spins are arranged on a complete graph, and the interaction coefficient J ij is assumed to occur between all spins, and the magnetic field is also allowed to be non-uniform. Physically, at low temperatures, the system often realizes a state {s i} i in which the Hamiltonian takes a small value, and J ij<0 (or, J ij >0), then spins i and j are likely to align (or, unlikely to align), H i >0 (or, H i <0), then spin variable s i is likely to take -1 (or, +1). Depending on the graph shape of the spin configuration and the magnitudes of various coefficients, it is not easy to obtain the lowest energy and its state (ground state), and it becomes a combinatorial optimization problem with many local optimal solutions.

[0018] Examples of computers using the above Ising model include, for example, a quantum annealing machine (Non-Patent Document 3), a coherent Ising machine (Non-Patent Document 4), etc. Hereinafter, these will be collectively referred to as Ising machines. An Ising machine is considered as a mechanism that gives the ground state and its energy of a system that can be expressed by the above Hamiltonian, and it is assumed that any Ising machine can be used.

[0019] If the combinatorial optimization problem can be converted into the form of the above Hamiltonian, then the lowest energy of the Hamiltonian and its ground state (that is, the minimum value of the objective function and the optimal solution) can be obtained using an Ising machine. Generally, as shown in the following Step1 to Step4, it often goes through the form of QUBO (unconstrained quadratic binary optimization).

[0020] Step1: Convert the combinatorial optimization problem into QUBO Step2: Convert QUBO into the form of an Ising Hamiltonian (that is, convert QUBO into an Ising model) Step3: Convert the Ising Hamiltonian into a form that can be solved by an Ising machine (that is, embed it in a physical model (embedding)) Step4: Execute the optimization Step 2 above is executed by variable conversion, and Step 3 above is executed according to a procedure specific to the Ising machine, but both can be realized with existing technology because tools that can execute them automatically have been developed. However, auxiliary bits may be required when embedding in the physical model in Step 3 above, and if there are limitations on the number of available bits, this point must be taken into consideration.

[0021] Therefore, if you want to solve the original combinatorial optimization problem, you should focus on Step 1 above.

[0022] QUBO is an optimization problem whose objective function is expressed in the form shown in the following equation (2).

[0023]

number

[0024] Hereinafter, a method for converting the monitoring path design problem in network tomography into HOBO or QUBO (that is, the method corresponding to the above Step 1) is proposed. This proposed method can be commonly applied to any annealing machine. Note that, as described above, Steps 2 to 3 can be realized by existing technologies such as automatic execution tools.

[0025] <<Problem Setting>> First, prepare mathematical terms and concepts.

[0026] · Graph representing the target network The target network is represented by a simple (that is, without multiple edges or loops) connected undirected graph G = (V, E). A node v ∈ V represents a network device such as a router, for example. Also, a link e ∈ E represents a link between network devices, for example. Note that a link e can also be regarded as a set of two different nodes.

[0027] Each link e ∈ E has a state (binary value) of either "normal" or "faulty". A link with a value representing "normal" is also called a "normal link", and a link with a value representing "faulty" is also called a "faulty link". Also, let N = |N| (total number of nodes) and M = |E| (total number of links).

[0028] · Monitoring path set P Let the set of monitoring paths p be the monitoring path set P. A monitoring path p ∈ P is a path on G (that is, a sequence of links connecting different nodes. However, it is assumed not to pass through the same node in the middle). A monitoring path p is represented as a set of links, for example, p = {e1, e2, ···, e m} ⊂ P.

[0029] If a monitoring path p contains a faulty link, p is called "abnormal". On the other hand, if a monitoring path p contains only normal links, p is called "normal".

[0030] Set P of monitoring paths that become abnormal when link e is faulty and other links are normale It is written as ⊂P. In the following, it is explained assuming that two links do not fail simultaneously, but even if there is a simultaneous failure, the formulation can be extended and this embodiment can be applied in the same way. Also, in the following, it is explained assuming that there is no node failure and only link failures can occur, but even if there is a node failure, the formulation can be extended and this embodiment can be applied in the same way.

[0031] As a representation method of the monitoring path set P, a monitoring path matrix B which is a binary matrix of |P| rows and M columns is defined. For the monitoring paths p1, p2, ···, p |P| , and for all links e1, e2, ···, e M Let's assign them in order. At this time, the (i, j) component of the monitoring path matrix B is B ij When p i includes e j , B ij = 1, and when p i does not include e j , B ij = 0.

[0032] ·distinguishability and identifiability Define distinguishability according to Non-Patent Document 2.

[0033] Assume that the monitoring path set P is given. When links e1, e2 ∈ E satisfy P e_1 ≠P e_2 (However, e_1 and e_2 represent e1 and e2 respectively), e1 and e2 are said to be distinguishable with respect to P.

[0034] Assume that the monitoring path set P is given. When a link e ∈ E is distinguishable from any other link e' ∈ E - {e} with respect to P, e is said to be identifiable with respect to P.

[0035] The set of links identifiable with respect to P is written as S(P).

[0036] If we consider the monitoring path matrix B as a vertical vector formed by arranging b1, b2, ···, b M then the fact that link e i is identifiable is equivalent to the fact that b i does not match any other vertical vector. Also, the number of identifiable links |S(P)| is nothing but the number of vertical vectors that do not match any other vertical vector among those constituting the monitoring path matrix B.

[0037] Monitoring path p i contains only one of e j and e k In other words, when B ij ≠B ik (or more precisely, when p i ∈P e_j and p i ∈P e_k (where ej and ek represent e j and e k respectively) and only one of them holds), the monitoring path p i is said to separate e j and e k .

[0038] In this embodiment, methods for the following two problems (i) and (ii) are provided. However, even if not strictly following this, problems similar to this can also be formulated and solved in the same way.

[0039] (i) Monitoring path selection problem Problem: Given a monitoring path set P and a natural number K (where K ≤ |P|). At this time, what is the subset of P with an element number of K that maximizes the number of identifiable links? That is,

[0040]

Number

[0041] This problem can be considered as the problem of selecting the most effective placement of monitoring paths in the sense of identifiable within the budget range (i.e., | ~ P| = K) when any routing rule is predetermined and the implementable monitoring paths are enumerated.

[0042] (ii) Monitoring Path Design Problem Problem: Suppose a natural number K is given. At this time, what is the set P of monitoring paths with the number of elements being K that maximizes the number of identifiable links? That is,

[0043]

Number

[0044] In this problem, there are no other restrictions on the monitoring path p ∈ P as long as it is a path on G. That is, under the condition that the routing rule can be freely set for each path, it can be considered as the problem of designing the most effective placement of monitoring paths in the sense of identifiable within the budget range (i.e., |P| = K).

[0045] ≪Details of the Proposed Method≫ For the above problems (i) and (ii), a method of expressing the objective function in the form of HOBO or QUBO will be described. Hereinafter, it is assumed that a simple connected undirected graph G = (V, E) representing the target network is given.

[0046] (i) Solution to the Monitoring Path Selection Problem This problem can be expressed as the minimization problem of the objective function E in the form of HOBO shown in the following formula (3) HOBO as follows.

[0047]

Number

[0048] At this time, the variable to be searched is {z i} i where z i takes 1 when the monitoring path p i is adopted as an element of P and 0 when not adopted (where i ∈ {1, 2, ···, |P|}). Among the above formula (3), the part (a) in Figure 1 means that when the monitoring path p ~ is adopted as an element of P, it becomes 0 if e i is separated by p ~ and 1 otherwise. The part (b) means that it becomes 1 if e i is separated by the monitoring path in P and 0 otherwise. The part (c) means that it becomes 1 if e j is identifiable by the monitoring path in P and 0 otherwise. The part (d) represents the number of identifiable links in P × (-1) and is the object of minimization (i.e., maximization of the number of identifiable links). The part (e) is the constraint condition that there are K monitoring paths included in P. k Note that in the annealing machine, generally, constraint conditions cannot be clearly specified. Therefore, as in the above formula (3), a penalty term λ > 0 is used to introduce a relaxation term so that the value of the objective function increases when the constraint condition is violated. If the value of λ is large enough, it becomes easier to obtain a solution that satisfies the constraint condition. However, since the value of λ depends on the performance of the annealing machine and also affects the optimality result of the obtained solution, it needs to be set appropriately. ~ The HOBO-form objective function E shown in the above formula (3) j is as follows. k Note that in the annealing machine, generally, constraint conditions cannot be clearly specified. Therefore, as in the above formula (3), a penalty term λ > 0 is used to introduce a relaxation term so that the value of the objective function increases when the constraint condition is violated. If the value of λ is large enough, it becomes easier to obtain a solution that satisfies the constraint condition. However, since the value of λ depends on the performance of the annealing machine and also affects the optimality result of the obtained solution, it needs to be set appropriately. ~ The HOBO-form objective function E shown in the above formula (3) j is as follows. ~ The part (d) represents the number of identifiable links in P × (-1) and is the object of minimization (i.e., maximization of the number of identifiable links). The part (e) is the constraint condition that there are K monitoring paths included in P. ~ is the constraint condition that there are K monitoring paths included in P.

[0049] Note that in the annealing machine, generally, constraint conditions cannot be clearly specified. Therefore, as in the above formula (3), a penalty term λ > 0 is used to introduce a relaxation term so that the value of the objective function increases when the constraint condition is violated. If the value of λ is large enough, it becomes easier to obtain a solution that satisfies the constraint condition. However, since the value of λ depends on the performance of the annealing machine and also affects the optimality result of the obtained solution, it needs to be set appropriately.

[0050] The HOBO-form objective function E shown in the above formula (3) HOBOAlthough it can also be converted into the QUBO format by a general methodology, in this embodiment, the objective function E in the QUBO format as explicitly shown in the following formula (4) is given. QUBO is also given.

[0051]

Number

[0052] At this time, the variables to be searched are as follows.

[0053] z i : A variable that takes 1 when the monitoring path p i is ~ adopted as an element of P and 0 when not adopted (where i ∈ {1, 2, ···, |P|}).

[0054] x j,α : Determined by z i . When the number of links that are not distinguishable from the link e ~ with respect to P is α, it takes 1, and 0 otherwise (where j ∈ {1, 2, ···, M}, α ∈ {0, 1, ···, M - 1}). j is a variable that takes 1 when the number of links that are not distinguishable from the link e

[0055] y j,k,m : Determined by z i . When the number of monitoring paths p ∈ ~ P included in P that separate the link e ~ from the link e j and e k is m, it takes 1, and 0 otherwise (where j, k ∈ {1, 2, ···, M}, m ∈ {0, 1, ···, |P|}).

[0056] Among the above formula (4), the part (a) in Figure 2 represents the number of identifiable links × (-1) and is the object to be minimized. The part (b) is x j,αRepresents the constraint conditions resulting from the definition. The part (U) is for x j,α and y j,k,0 The constraint condition (link e j and the number of links that are not distinguishable from it). The part (E) is the constraint condition resulting from the definition of y j,k,m . The part (O) is the constraint condition (the equation regarding the number of monitoring paths that separate link e j,k,m and z i ) representing the relationship between y j and e k . The part (KA) is ~ The constraint condition that the number of monitoring paths included in P is K

[0057] Note that in the above formula (4), the common weight λ is used for the relaxation terms of the constraint conditions, but different values may be adopted respectively

[0058] (ii) Solution to the monitoring path design problem The objective function for this problem must reflect the constraint condition that the monitoring path p ∈ P is a path on G. For this, some preparations are made

[0059] Definition (link-induced subgraph): A subgraph G'=(V',E') of an undirected graph G=(V,E) where V'={v∈V'|∃e∈E',v∈e} is called a link-induced subgraph of G

[0060] Lemma 1: The necessary and sufficient condition for the link-induced subgraph G'=(V',E') of an undirected graph G=(V,E) to be a path on G (exactly, it becomes a path on G when an appropriate sequence is made with the links in E') is to satisfy the following two conditions

[0061] · Condition 1-1: In G', exactly two vertices have degree 1, and the other vertices have degree 2

[0062] · Condition 1-2: G' has no cycles

[0063] Since Lemma 1 is obvious, its proof is omitted.

[0064] Lemma 2: A necessary and sufficient condition for an undirected graph G = (V, E) to have no cycles is that there exist a node height function h: V → {0, 1, ···, N - 1} and a link height function h': E → {1, 2, ···, N - 1} that satisfy the following three conditions.

[0065] · Condition 2-1: For all nodes u, v ∈ V, when u and v are adjacent, |h(v) - h(u)| = 1.

[0066] · Condition 2-2: For all links e = {v e 0 , v e 1} ∈ E, h'(e) = max{h(v e 0 ), h(v e 1 )} holds.

[0067] · Condition 2-3: For all nodes v ∈ V, among the links {e v i} i connected to v, there is at most one such that h'(e v i ) = h(v).

[0068] (Proof) Necessity: It suffices to show the existence of functions h and h' when the undirected graph G is a tree. Let any v0 ∈ V be the root with h(v0) = 0. For the other nodes v ∈ V - {v0}, let the height of each node (the length of the path to the root) be h(v), and define h' so that Condition 2-2 is satisfied. Then Conditions 2-1 and 2-3 are satisfied. Sufficiency: Assume that there exist functions h and h' that satisfy Conditions 2-1, 2-2, and 2-3. Suppose G has a cycle (v0, v1, ···, v n , v0),

[0069]

Number

[0070] Lemma 3: A necessary and sufficient condition for an undirected graph G=(V,E) to have no cycle is that there exist a node height function h:V→{0,1,···,N-1} and a directed link height function ~ h: ~ E→{0,1,2,···,N-1}. However, ~ E is the set of the directed versions of the links. That is, ~ E={(u,v)|∃e∈E,u∈e,v∈e,u≠v}.

[0071] Condition 3-1: For all nodes u,v∈V, when u and v are adjacent, |h(v)-h(u)| = 1.

[0072] Condition 3-2: For all links e={v e 0 ,v e 1}∈E, if h(v e 0 )≧h(v e 1 ), then ~ h((v e 0 ,v e 1 )) = 0, ~ h((v e 1 ,v e 0 )) = h(v e 0 ) holds, and if h(v e 0 ) < h(v e 1 ), then ~ h((v e 0 ,v e 1 )) = h(v e1 ) ~ h((v e 1 , v e 0 )) = 0 holds.

[0073] Condition 3-3: For all nodes v ∈ V, among the directed links { ~ e v i}} i such that ~ h( ~ e v i ) = h(v), if h(v) ≠ 0, there is at most one.

[0074] (Proof) Necessity: From Lemma 2, there exist h and h' that satisfy Conditions 2-1, 2-2, and 2-3. At this time, for the link e = (u, v), if h(u) ≥ h(v), then ~ h((u, v)) = 0, ~ h((v, u)) = h'({u, v}), if h(u) < h(v), then ~ h((u, v)) = h'({u, v}), ~ h((v, u)) = 0, and by defining the directed link height function ~ h, ~ h satisfies Conditions 3-1, 3-2, and 3-3. Sufficiency: Assume that there exists a function h, ~ h that satisfies Conditions 3-1, 3-2, and 3-3. At this time, for the link e = {u, v}, if we define the link height function h' by h'(e) = max{ ~ h(u, v), ~ h(v, u)}, then h and h' satisfy Conditions 2-1, 2-2, and 2-3. Therefore, from Lemma 2, G = (V, E) has no cycles.

[0075] From the above, to ensure that the monitoring path p ∈ P is a path on G, it can be seen that it is necessary to require that Condition 1-1 of Lemma 1 holds and there exist functions h, ~ h that satisfy Conditions 3-1 to 3-3 of Lemma 3. Based on these, this problem is the QUBO-form objective function E shown in the following formula (5)QUBO can be expressed as a minimization problem.

[0076]

Number

[0077] At this time, the variables to be searched are as follows. However, P is a provisional solution of the set of monitoring paths.

[0078] x j,α : Regarding P, a variable that takes 1 when the number of links that are not distinguishable from link e j is α, and 0 otherwise (where j ∈ {1, 2, ···, M}, α ∈ {0, 1, ···, M - 1}).

[0079] y j,k;m : A variable that takes 1 when the number of monitoring paths p ∈ P that separate link e j and e k is m, and 0 otherwise (where j, k ∈ {1, 2, ···, M}, m ∈ {0, 1, ···, K}).

[0080] s i;j,k;m : For monitoring path p i ∈ P, if both link e j and e k are included or neither is included, then s i;j,k;0 = 1; if only link e j is included, then s i;j,k;1 = 1; if only link e k is included, then s i;j,k;-1 = 1 (where i ∈ {1, 2, ···, K}, j, k ∈ {1, 2, ···, M}, m ∈ {0, 1, -1}).

[0081] q ij : For monitoring path pi A variable that takes 1 when link e is included in P and 0 otherwise (where i ∈ {1, 2, ···, K}, j ∈ {1, 2, ···, M}). j A variable that takes 1 when the degree of node v is m with respect to the sub - graph p which is a candidate for the monitoring path but not necessarily a path, and 0 otherwise (where i ∈ {1, 2, ···, K}, l ∈ {1, 2, ···, N}, m ∈ {0, 1, 2}).

[0082] r i;l,m : A sub - graph p which is a candidate for the monitoring path but not necessarily a path i For node v l A variable that takes 1 when the degree of node v is m with respect to the sub - graph p which is a candidate for the monitoring path but not necessarily a path, and 0 otherwise (where i ∈ {1, 2, ···, K}, l ∈ {1, 2, ···, N}, m ∈ {0, 1, 2}).

[0083] h i;l,β : For the sub - graph p i For node v l A variable that takes 1 when the value of the height function h(v l ) is β with respect to the sub - graph p, and 0 otherwise (where i ∈ {1, 2, ···, K}, l ∈ {1, 2, ···, N}, β ∈ {0, 1, ···, N - 1}).

[0084] ~ h i;l,l';β : For the sub - graph p i A variable that takes 1 when the value of the height function of the directed link h((v l , v l ') for the directed link (v ~ h((v l , v l ')) is β with respect to the sub - graph p, and 0 otherwise (where i ∈ {1, 2, ···, K}, l, l' ∈ {1, 2, ···, N}, β ∈ {1, ···, N - 1}).

[0085] Among the above formula (5), the part (a) in Figure 3 represents the number of identifiable links × (- 1) and is the object of minimization. The part (b) represents the constraint conditions resulting from the definitions of x j,α , y j,k;m , s i;j,k;m . (c - 1) to (c - 3) are constraint conditions representing the relationships that hold between the variables. The part of (c - 1) is for link e jIt is an equation regarding the number of links that are not distinguishable. The part of (u - 2) is the equation regarding the number of monitoring paths that separate link e j and e k It is an equation regarding the number of monitoring paths that separate link e. The part of (u - 3) is the equation regarding whether monitoring path p i includes link e j and e k It is an equation that represents whether it includes e. (ε - 1) to (ε - 3) are the constraint conditions regarding the degree of vertices and correspond to condition 1 - 1 of Lemma 1. The part of (ε - 1) represents that all vertices have a degree of 0, 1, or 2. The part of (ε - 2) represents that a degree of 0 is a node outside the monitoring path, a degree of 1 is a node at both ends of the monitoring path, and a degree of 2 is a node inside the monitoring path and other than both ends. The part of (ε - 3) represents that exactly two nodes have a degree of 1. (ω - 1) to (ω - 3) are the constraint conditions regarding that the monitoring path has no closed loop and correspond to condition 1 - 2 of Lemma 1. The part of (ω - 1) is the constraint condition resulting from the definition of the node height function, which represents that for a node inside the monitoring path, the node height function gives an integer value within [0, β - 1], and for a node outside the monitoring path, the node height function is not defined. The part of (ω - 2) is the constraint condition resulting from the definition of the directed link height function, which represents that for a link inside the monitoring path, one of the two directed link height functions gives an integer value within [1, N - 1] and the other gives 0, and for a link outside the monitoring path, the directed link height function is not defined. The part of (ω - 3) corresponds to condition 3 - 3 of Lemma 3. The part of (ω - 4) corresponds to condition 3 - 1 and condition 3 - 2 of Lemma 3.

[0086] Note that in the above formula (5), a common weight λ is used for the relaxation terms of the constraint conditions, but different values may be adopted respectively.

[0087] <Hardware configuration example of monitoring path design device 10> A hardware configuration example of the monitoring path design device 10 according to this embodiment is shown in FIG. 4. As shown in FIG. 4, the monitoring path design device 10 according to this embodiment includes an input device 11, a display device 12, an external I / F 13, a communication I / F 14, a RAM (Random Access Memory) 15, a ROM (Read Only Memory) 16, an auxiliary storage device 17, and a processor 18. These pieces of hardware are each communicably connected via a bus 19.

[0088] The input device 11 is, for example, a keyboard, a mouse, a touch panel, a physical button, etc. The display device 12 is, for example, a display, a display panel, etc. Note that the monitoring path design device 10 may not have at least one of the input device 11 and the display device 12, for example.

[0089] The external I / F 13 is an interface with an external device such as a recording medium 13a. The monitoring path design device 10 can read and write to the recording medium 13a via the external I / F 13. Examples of the recording medium 13a include a flexible disk, a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), a USB (Universal Serial Bus) memory card, etc.

[0090] The communication I / F 14 is an interface for connecting the monitoring path design device 10 to a communication network. The RAM 15 is a volatile semiconductor memory (storage device) that temporarily holds programs and data. The ROM 16 is a non-volatile semiconductor memory (storage device) that can hold programs and data even when the power is turned off. The auxiliary storage device 17 is a storage device (storage device) such as an HDD (Hard Disk Drive), an SSD (Solid State Drive), a flash memory, etc., for example. The processor 18 is an arithmetic device such as a CPU (Central Processing Unit), for example.

[0091] The monitoring path design device 10 according to this embodiment can realize the monitoring path design process described later by having the hardware configuration shown in FIG. 4. Note that the hardware configuration shown in FIG. 4 is an example, and the hardware configuration of the monitoring path design device 10 is not limited to this. For example, the monitoring path design device 10 may have a plurality of auxiliary storage devices 17 and a plurality of processors 18, may not have a part of the illustrated hardware, or may have various hardware other than the illustrated hardware.

[0092] <Example of the functional configuration of the monitoring path design device 10> An example of the functional configuration of the monitoring path design device 10 according to this embodiment is shown in FIG. 5. As shown in FIG. 5, the monitoring path design device 10 according to this embodiment includes a graph creation unit 101, an objective function design unit 102, a Hamiltonian creation unit 103, and a user interface unit 104. Note that the topology information of the target network, the parameters (such as λ and K) and the constraint conditions of the monitoring path selection problem shown in (i) above or the monitoring path design problem shown in (ii) above are given to the monitoring path design device 10. Note that the topology information is information representing the network devices included in the target network and their connection relationships.

[0093] The graph creation unit 101 creates an undirected graph G (specifically, a simple connected undirected graph G) from the given topology information.

[0094] The objective function design unit 102 creates an objective function in the HOBO format or the QUBO format using the undirected graph G created by the graph creation unit 101 and the given parameters and constraint conditions. That is, when the objective function design unit 102 solves the monitoring path selection problem shown in (i) above, the objective function E shown in the above formula (3) HOBO or the objective function E shown in formula (4) QUBO is created, and when solving the monitoring path design problem shown in (ii) above, the objective function E shown in the above formula (5) QUBO is created.

[0095] The Hamiltonian creation unit 103 converts the objective function created by the objective function design unit 102 into an Ising Hamiltonian, and then converts it into a format that can be solved by the computing device 20, which is an Ising machine. That is, the Hamiltonian creation unit 103 performs the processes related to the above Step2 and Step3. Hereinafter, the Ising Hamiltonian converted into a format that can be solved by the computing device 20 is referred to as the post-conversion Ising Hamiltonian. Note that the Hamiltonian creation unit 103 may, if necessary, lower the degree of the objective function in the HOBO format to the QUBO format, and then convert this QUBO format objective function into an Ising Hamiltonian.

[0096] Also, the Hamiltonian creation unit 103 transmits the post-conversion Ising Hamiltonian to the computing device 20. As a result, an optimal monitoring path set is obtained as an optimal solution (quasi-optimal solution closer to the correct answer) by the computing device 20, which is an Ising machine.

[0097] The user interface unit 104 displays the optimal monitoring path set calculated by the computing device 20 on a user interface such as the display device 12. Note that this is not limited thereto, and the user interface unit 104 may, for example, save the optimal monitoring path set in the auxiliary storage device 17 or the like.

[0098] Note that in the example shown in FIG. 5, the computing device 20, which is an Ising machine, exists outside the monitoring path design device 10, but this is not limiting, and the monitoring path design device 10 may include a computing unit that functions as an Ising machine.

[0099] <Monitoring Path Design Process> The flow of the monitoring path design process according to the present embodiment will be described with reference to FIG. 6.

[0100] The graph creation unit 101 creates an undirected graph G from the given topology information (step S101).

[0101] Next, the objective function design unit 102 creates an objective function in the HOBO format or the QUBO format (the objective function shown in Equation (3) or Equation (4), or the objective function shown in Equation (5)) using the undirected graph G created in the above step S101, the given parameters, and the constraint conditions (step S102).

[0102] Next, the Hamiltonian creation unit 103 converts the objective function in the HOBO format or the QUBO format created in the above step S102 into an Ising Hamiltonian, and then converts it into a format that can be solved by the computing device 20, which is an Ising machine (step S103). Thereby, the converted Ising Hamiltonian is created.

[0103] Next, the Hamiltonian creation unit 103 transmits the converted Ising Hamiltonian created in the above step S103 to the computing device 20 (step S104). Thereby, using the converted Ising Hamiltonian, the optimal monitoring path set is calculated as the optimal solution by the computing device 20.

[0104] Then, the user interface unit 104 displays the optimal monitoring path set calculated by the computing device 20 on a user interface such as the display device 12 (step S105).

[0105] <Summary> As described above, the monitoring path design apparatus 10 according to the present embodiment formulates the problem of maximizing the objective function indicating the effectiveness of the monitoring path into a form that can be solved by an annealing machine called HOBO or QUBO. As a result, any annealing machine can obtain a quasi-optimal solution that is considered to have higher network state segmentation performance. In an annealing machine, it is considered that a solution superior to the existing technology can be discovered because the entire search space is widely searched for the optimal solution. In addition, many calculation examples showing higher performance than classical computers have been reported for annealing machines, and it is expected that even larger-scale calculations will be possible as the number of available qubits increases in the future. Therefore, even in the case of a large-scale network system that could not be handled by the prior art, it is possible to design a monitoring path with higher performance, and the realization of high-quality network operation can be expected.

[0106] The present invention is not limited to the specifically disclosed above embodiments, and various modifications, changes, combinations with known technologies, etc. are possible without departing from the scope of the claims.

Explanation of Signs

[0107] 10 Monitoring path design apparatus 11 Input device 12 Display device 13 External I / F 13a Recording medium 14 Communication I / F 15 RAM 16 ROM 17 Auxiliary storage device 18 Processor 19 Bus 20 Computing device 101 Graph creation unit 102 Objective function design unit 103 Hamiltonian creation unit 104 User interface unit

Claims

1. A monitoring path design device for designing a monitoring path for estimating the state of a target network, An objective function creation unit configured to create, in a form computable by an Ising machine, an objective function representing the effectiveness of the monitoring path using an undirected graph representing the topology of the target network, A monitoring path design device having the above.

2. The effectiveness of the monitoring path is the segmentation performance of the state of the target network, The objective function creation unit, For the problem of selecting a set of monitoring paths with high segmentation performance of the state of the target network from among a plurality of monitoring path candidates under given constraint conditions, the HOB0 format or QUBO format of the function to be optimized in the problem is used as the objective function. The monitoring path design device according to claim 1, which is configured to create as

3. The effectiveness of the monitoring path is the segmentation performance of the state of the target network, The objective function creation unit, For the problem of designing a set of monitoring paths with high segmentation performance of the state of the target network under given constraint conditions, the QUBO format of the function to be optimized in the problem is used as the objective function. The monitoring path design device according to claim 1, which is configured to create as

4. A user interface unit configured to output, to a user interface, a set of monitoring paths calculated by the Ising machine from the objective function created by the objective function creation unit. The monitoring path design device according to any one of claims 1 to 3, further comprising

5. A monitoring path design device for designing a monitoring path for estimating the state of a target network, An objective function creation procedure for creating, in a form computable by an Ising machine, an objective function representing the effectiveness of the monitoring path using an undirected graph representing the topology of the target network, A monitoring path design method for executing **Claim 6** In a monitoring path design device for designing a monitoring path for estimating the state of a target network, An objective function creation procedure for creating, in a form computable by an Ising machine, an objective function representing the effectiveness of the monitoring path using an undirected graph representing the topology of the target network, A program for causing the above to be executed.

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