We present a framework for an automated generation of exact search tree algorithms for NP-hard problems. The purpose of our approach is twofold-rapid development and improved upper bounds. Many search tree algorithms ...
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We present a framework for an automated generation of exact search tree algorithms for NP-hard problems. The purpose of our approach is twofold-rapid development and improved upper bounds. Many search tree algorithms for various problems in the literature are based on complicated case distinctions. Our approach may lead to a much simpler process of developing and analyzing these algorithms. Moreover, using the sheer computing power of machines it may also lead to improved upper bounds on searchtree sizes (i.e., faster exact solving algorithms) in comparison with previously developed "hand-made" searchtrees. Among others, such an example is given with the NP-complete Cluster Editing problem (also known as Correlation Clustering on complete unweighted graphs), which asks for the minimum number of edge additions and deletions to create a graph which is a disjoint union of cliques. The hand-made searchtree for Cluster Editing had worst-case size O(2.27(k)), which now is improved to O(1.92(k)) due to our new method. (Herein, k denotes the number of edge modifications allowed.).
Backtracking branch-and-prune (BP) algorithms and their variants are exhaustive searchtree techniques widely employed to solve optimization problems in many scientific areas. However, they characteristically often de...
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Backtracking branch-and-prune (BP) algorithms and their variants are exhaustive searchtree techniques widely employed to solve optimization problems in many scientific areas. However, they characteristically often demand significant amounts of computing power for problem sizes representative of real-world scenarios. Given that their search domains can often be partitioned, these algorithms are frequently designed to execute in parallel by harnessing distributed computing systems. However, to achieve efficient parallel execution times, an effective strategy is required to balance the nonuniform partition workloads across the available resources. Furthermore, with the increasing integration of servers with heterogeneous resources and the adoption of resource sharing, balancing workloads is becoming complex. This paper proposes a strategy to execute parallel BP algorithms more efficiently on even shared or heterogeneous distributed systems. The approach integrates a self-adjusting dynamic partitioning method in the BP algorithm with a dynamic scheduler, provided by an application middleware, which manages the parallel execution while addressing any issues of imbalance. Empirical results indicate better scalability with efficiencies above 90% for instances of an application case study for the discretizable molecular distance geometry problem (DMDGP). Improvements of up to 38% were obtained in execution speed-ups compared to a more traditional parallel BP implementation for DMDGP.
We are going to analyze search tree algorithms for WEIGHTED d-HITTING SET. Although the algorithms that we develop are fairly simple, their analysis is technically involved. We compare the weighted case with the previ...
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We are going to analyze search tree algorithms for WEIGHTED d-HITTING SET. Although the algorithms that we develop are fairly simple, their analysis is technically involved. We compare the weighted case with the previously analyzed unweighted one, exhibiting that the advantage of the unweighted case dwindles with growing d. (C) 2010 Elsevier B.V. All rights reserved.
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