Dynamic Range Data Structure for Constraint Solvers
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Solution Overview
Problem
Existing methods for representing variable domains in constraint problems are inefficient, particularly when dealing with large numeric sets, as they require significant memory and are not optimized for complex constraint solver algorithms.
Innovation Solution
A self-optimizing data structure that consolidates adjacent and overlapping ranges by storing upper and lower bounds, allowing for efficient representation and manipulation of ranges of values, reducing memory usage and computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional methods are used to represent variable domains in constraint problems, then complete representation of all numeric values is achieved, but memory usage becomes excessive and computational efficiency deteriorates
Solution Approach 1:
The patent segments the continuous numeric domain into discrete intervals or ranges, where each node represents a specific interval [lower_bound, upper_bound]. This segmentation allows the system to represent large domains using fewer discrete units, reducing memory consumption while maintaining complete domain coverage through the union of all node intervals.
Solution Approach 2:
The patent transforms the one-dimensional representation of individual numeric values into a two-dimensional structure by introducing the concept of intervals with lower and upper bounds. Each node represents a range rather than a single value, adding the dimension of span or range to the data structure, which enables more compact representation of large domains.
2Measurement precision
If all individual numeric values are stored separately, then precise domain representation is achieved, but data structure complexity and processing overhead increase
Solution Approach 1:
The patent merges adjacent and overlapping intervals by consolidating them into single nodes. When two nodes represent contiguous or overlapping ranges, they are merged into one node representing the union of both intervals. This merging operation reduces the total number of nodes in the data structure while preserving the complete domain representation, thereby reducing complexity.
Solution Approach 2:
The patent creates a universal node structure that can represent any numeric interval regardless of its specific bounds. Each node serves multiple functions: representing a range, enabling intersection/union operations, and participating in constraint satisfaction checks. This multi-functionality reduces the need for specialized data structures for different operations.
3Adaptability or versatility
If redundant overlapping ranges are maintained in the data structure, then flexibility in representing complex domains is preserved, but memory efficiency and processing speed deteriorate
Solution Approach 1:
The patent implements a dynamic data structure where nodes are automatically merged or split based on the current state of domain representation. As constraints are applied and domains are reduced, the structure dynamically adapts by merging newly adjacent intervals and splitting intervals when necessary to maintain the non-overlapping property. This dynamic behavior maintains flexibility while optimizing for efficiency at each step of the constraint solving process.
Data Source
AI summary
A method of efficiently representing ranged data sets may include storing a data structure representing a first data set. The data structure may include one or more nodes each representing distinct portions of the data set, and the first data set may include a range of multiple values bounded by an upper bound and a lower bound. A first node may represent the range of multiple values by storing the upper bound and the lower bound. The method may also include receiving a second data set to add to the first data set. The intersection of the first data set and the second data may include at least one value. The method may further include altering the one or more nodes in the data structure such that the union of each of the distinct portions of the data set represented by the one or more nodes is equivalent to the union of the first data set and the second data set; and such that the intersection of each of the distinct portions of the data set represented by the one or more nodes is equivalent to an empty data set.