Multiset Encoding via Prime Number Product
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Solution Overview
Problem
Efficient storage and maintenance of multisets in security analytics scenarios, particularly in user and entity behavioral analytics, is challenging due to high storage costs and the need for efficient insertion and removal of entities, which existing technologies have not adequately addressed.
Innovation Solution
Encoding multisets as products of prime numbers assigned to entities, allowing for efficient insertion and removal through integer multiplication and division, and identifying entities by decomposing integer representations into prime factors, with a mapping between entities and prime numbers for efficient data retrieval.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If traditional data structures are used to store multisets, then the storage cost becomes high, but the efficiency of insertion and removal operations is reduced
Solution Approach 1:
The patent transforms the multiset data structure into a different parameter space by encoding it as an integer product of prime numbers. This parameter transformation allows both compact storage (reducing space complexity) and efficient operations (multiplication for insertion, division for removal) to be performed using basic arithmetic operations.
Solution Approach 2:
The patent replaces traditional mechanical data structure operations (such as array insertions, deletions, and set manipulations) with arithmetic operations. Instead of moving and reorganizing data elements in memory, the system uses multiplication and division of integers, which are computationally more efficient and require less memory management overhead.
2Productivity
If multisets are maintained with efficient insertion and removal, then operational efficiency is improved, but storage complexity increases
Solution Approach 1:
The patent simplifies the storage structure by transforming complex multiset data into a single integer parameter. This parameter change reduces storage complexity from needing to maintain multiple data structures (for efficient operations) to simply storing one integer value, while preserving all multiset information through prime factorization.
3Speed
If real-time identification of user-device connections is implemented, then query speed is improved, but computational complexity increases
Solution Approach 1:
The patent replaces complex query processing mechanisms (such as iterating through stored connections or performing set operations) with simple arithmetic operations. By encoding the multiset as an integer product, identification operations become straightforward division and factorization tasks, significantly reducing computational complexity while maintaining real-time query capability.
Data Source
AI summary
Techniques are provided for multiset encoding and evaluation. One method comprises encoding a multi set comprised of entities as a product of a prime number assigned to each entity in the multiset to obtain an integer representation of the multiset; adding a first entity to the multiset by multiplying the integer representation of the multiset by the prime number assigned to the first entity; removing a second entity from the multiset by dividing the integer representation of the multiset by the prime number assigned to the second entity; and identifying the entities in the multi set by decomposing the integer representation into a product of the prime numbers assigned to each of the entities in the multiset. The entities in the multiset can be, for example, devices that a given user was connected to at the given time; and/or the users connected to a given device at the given time.