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Upper and lower bounding procedures for minumum rooted k-subtree problem

Article Abstract:

The minimum rooted k-subtree problem is explained and procedures for developing a lower bound are set out, with computational results analyzed.

Algebra, K-theory, K theory

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A heuristic algorithm for the mini-max spanning forest problem

Article Abstract:

A heuristic algorithm is developed for the mini-max spanning forest problem for undirected graphs. The problem is considered as a generalization of the minimum spanning tree problem. Evidence is given that the problem is NP-hard. The heuristic algorithm can provide an approximate solution and can provide an upper bound for relative errors. A number of numerical experiments are conducted to test the performance of the algorithm.

Usage, Heuristic programming, Graph theory, Trees (Graph theory)

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Some exact algorithms for the knapsack sharing problem

Article Abstract:

Two algorithms, a branch-and-bound algorithm and a binary search algorithm, were evaluated in terms of solving the knapsack sharing problem (KSP). Computational experiments and implementation of the two algorithms were undertaken to assess their behavior. Of the two algorithms developed, the binary search algorithm was able to solve KSPs ranging up to 20000 variables in less than 60 seconds.

Combinatorial optimization, Binary searching

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