The Minimum Weight In-Tree Cover Problem

2008 ◽  
pp. 155-164
Author(s):  
Naoyuki Kamiyama ◽  
Naoki Katoh
Keyword(s):  
Minimum Weight ◽  
Tree Cover ◽  
Cover Problem

scholarly journals Parameterized Analysis of Multiobjective Evolutionary Algorithms and the Weighted Vertex Cover Problem

2019 ◽  
Vol 27 (4) ◽  
pp. 559-575
Author(s):  
Mojgan Pourhassan ◽  
Feng Shi ◽  
Frank Neumann
Keyword(s):  
Evolutionary Algorithm ◽  
Complexity Analysis ◽  
Minimum Weight ◽  
Vertex Cover ◽  
Optimal Solution ◽  
Population Based ◽  
Mutation Operator ◽  
Vertex Cover Problem ◽  
Weighted Vertex ◽  
Cover Problem

Evolutionary multiobjective optimization for the classical vertex cover problem has been analysed in Kratsch and Neumann ( 2013 ) in the context of parameterized complexity analysis. This article extends the analysis to the weighted vertex cover problem in which integer weights are assigned to the vertices and the goal is to find a vertex cover of minimum weight. Using an alternative mutation operator introduced in Kratsch and Neumann ( 2013 ), we provide a fixed parameter evolutionary algorithm with respect to [Formula: see text], the cost of an optimal solution for the problem. Moreover, we present a multiobjective evolutionary algorithm with standard mutation operator that keeps the population size in a polynomial order by means of a proper diversity mechanism, and therefore, manages to find a 2-approximation in expected polynomial time. We also introduce a population-based evolutionary algorithm which finds a [Formula: see text]-approximation in expected time [Formula: see text].

A HYBRID HEURISTIC FOR THE MINIMUM WEIGHT VERTEX COVER PROBLEM

2006 ◽  
Vol 23 (02) ◽  
pp. 273-285 ◽  
Author(s):  
ALOK SINGH ◽  
ASHOK KUMAR GUPTA
Keyword(s):  
Genetic Algorithm ◽  
Undirected Graph ◽  
Minimum Weight ◽  
Vertex Cover ◽  
Hybrid Approach ◽  
Greedy Heuristic ◽  
Test Problems ◽  
Minimal Weight ◽  
Vertex Cover Problem ◽  
Cover Problem

Given an undirected graph with weights associated with its vertices, the minimum weight vertex cover problem seeks a subset of vertices with minimum sum of weights such that each edge of the graph has at least one endpoint belonging to the subset. In this paper, we propose a hybrid approach, combining a steady-state genetic algorithm and a greedy heuristic, for the minimum weight vertex cover problem. The genetic algorithm generates vertex cover, which is then reduced to minimal weight vertex cover by the heuristic. We have evaluated the performance of our algorithm on several test problems of varying sizes. Computational results show the effectiveness of our approach in solving the minimum weight vertex cover problem.

Multi-start iterated tabu search for the minimum weight vertex cover problem

2015 ◽  
Vol 32 (2) ◽  
pp. 368-384 ◽  
Author(s):  
Taoqing Zhou ◽  
Zhipeng Lü ◽  
Yang Wang ◽  
Junwen Ding ◽  
Bo Peng
Keyword(s):  
Tabu Search ◽  
Minimum Weight ◽  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Cover Problem ◽  
Iterated Tabu Search

Constant-approximation for minimum weight partial sensor cover

2020 ◽  
pp. 2150047
Author(s):  
Siwen Liu ◽  
Hongmin W. Du
Keyword(s):  
Time Constant ◽  
Polynomial Time ◽  
Wireless Sensors ◽  
Minimum Weight ◽  
Total Weight ◽  
Sensor Cover ◽  
Nonnegative Weight ◽  
Cover Problem

Consider a set of homogeneous wireless sensors, [Formula: see text] with nonnegative weight [Formula: see text] for each sensor [Formula: see text]. Let [Formula: see text] be a set of target points. Given a integer [Formula: see text], we study the minimum weight partial sensor cover problem, that is, find the minimum total weight subset of sensors covering at least [Formula: see text] target points in [Formula: see text]. In this paper, we show the existence of polynomial-time constant-approximation for this problem.

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