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Disjoint-set data structures [9] and partition refinement [10] are two techniques in computer science for efficiently maintaining partitions of a set subject to, respectively, union operations that merge two sets or refinement operations that split one set into two. A disjoint union may mean one of two things. Most simply, it may mean the union ...
For many problems, relaxing the equality of split variables allows the system to be broken down, enabling each subsystem to be solved separately. This significantly reduces computation time and memory usage. Solving the relaxed problem with variable splitting can give an approximate solution to the initial problem.
Therefore, the remaining 3-sets can be partitioned into two groups: n 3-sets containing the items u ij, and n 3-sets containing the items u ij '. In each matching pair of 3-sets, the sum of the two pairing items u ij +u ij ' is 44T+4, so the sum of the four regular items is 84T+4. Therefore, from the four regular items, we construct a 4-set in ...
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S 1 and S 2 such that the sum of the numbers in S 1 equals the sum of the numbers in S 2.
In computational complexity theory, the set splitting problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists a partition of S into two subsets S 1, S 2 such that all elements of F are split by this partition, i.e., none of the elements of F is completely in S 1 or S 2.
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Once that page is full, the data is split into two sets that should cover the minimal area each. Most of the research and improvements for R-trees aims at improving the way the tree is built and can be grouped into two objectives: building an efficient tree from scratch (known as bulk-loading) and performing changes on an existing tree ...
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