Journal ArticleDOI
Greedy heuristics for the bounded diameter minimum spanning tree problem
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TLDR
On Euclidean problem instances with small diameter bounds, the randomized heuristic is superior to the two fully greedy algorithms, though its advantage fades as the diameter bound grows.Abstract:
Given a connected, weighted, undirected graph G and a bound D, the bounded diameter minimum spanning tree problem seeks a spanning tree on G of minimum weight among the trees in which no path between two vertices contains more than D edges. In Prim's algorithm, the diameter of the growing spanning tree can always be known, so it is a good starting point from which to develop greedy heuristics for the bounded diameter problem. Abdalla, Deo, and Gupta described such an algorithm. It imitates Prim's algorithm but avoids edges whose inclusion in the spanning tree would violate the diameter bound. Running the algorithm from one start vertex requires time that is O(n3).A modification of this approach uses the start vertex as the center of the spanning tree (if D is even) or as one of the two center vertices (if D is odd). This yields a simpler algorithm whose time is O(n2). A further modification chooses each next vertex at random rather than greedily, though it still connects each vertex to the growing tree with the lowest-weight feasible edge. On Euclidean problem instances with small diameter bounds, the randomized heuristic is superior to the two fully greedy algorithms, though its advantage fades as the diameter bound grows. On instances whose edge weights have been chosen at random, the fully greedy algorithms outperform the randomized heuristic.read more
Citations
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PHAST: Hardware-accelerated shortest path trees
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Efficient execution plans for distributed skyline query processing
TL;DR: A novel framework, called SkyPlan, for processing distributed skyline queries that generates execution plans aiming at optimizing the performance of query processing that consistently outperforms the state-of-the-art algorithm.
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LS(Graph): a constraint-based local search for constraint optimization on trees and paths
TL;DR: A constraint- based local search framework for COT/COP applications is proposed, bringing the compositionality, reuse, and extensibility at the core of constraint-based local search and constraint programming systems.
Book ChapterDOI
(Meta-)Heuristic Separation of Jump Cuts in a Branch&Cut Approach for the Bounded Diameter Minimum Spanning Tree Problem
Martin Gruber,Günther R. Raidl +1 more
TL;DR: This work solves a strong integer linear programming formulation based on so-called jump inequalities by a Branch&Cut algorithm, and introduces a new type of cuts, the center connection cuts, to strengthen the formulation in the more difficult to solve odd diameter case.
Proceedings ArticleDOI
New heuristic and hybrid genetic algorithm for solving the bounded diameter minimum spanning tree problem
TL;DR: A new heuristic, called Center-Based Recursive Clustering - CBRC, is proposed for solving the bounded diameter minimum spanning tree (BDMST) problem and the proposed hybrid genetic algorithm is extended to include thenew heuristic and a multi-parent crossover operator.
References
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