Worst-case behavior of the MVCA heuristic for the minimum labeling spanning tree problem

Xiong, Yupei; Golden, Bruce L.; Wasil, Edward

doi:10.1016/j.orl.2004.03.004

Cited by 38 publications

(24 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The versions of the present GA both resemble and differ from the algorithm of Xiong, Golden, and Wasil [9]. The latter algorithm should be included in the comparisons.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

An effective genetic algorithm for the minimum-label spanning tree problem

Nummela

Julstrom

2006

Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation

View full text Add to dashboard Cite

Given a connected, undirected graph G with labeled edges, the minimum-label spanning tree problem seeks a spanning tree on G to whose edges are attached the smallest possible number of labels. A greedy heuristic for this NP-hard problem greedily chooses labels so as to reduce the number of components in the subgraphs they induce as quickly as possible. A genetic algorithm for the problem encodes candidate solutions as permutations of the labels; an initial segment of such a chromosome lists the labels that appear on the edges in the chromosome's tree. Three versions of the GA apply generic or heuristic crossover and mutation operators and a local search step. In tests on 27 randomly-generated instances of the minimum-label spanning tree problem, versions of the GA that apply generic operators, with and without the local search step, perform less well than the greedy heuristic, but a version that applies the local search step and operators tailored to the problem returns solutions that require on average 10% fewer labels than the heuristic's.

show abstract

“…The versions of the present GA both resemble and differ from the algorithm of Xiong, Golden, and Wasil [9]. The latter algorithm should be included in the comparisons.…”

Section: Resultsmentioning

confidence: 99%

“…In particular, they showed that it returned results within a factor of (2 ln n + 1) of optimum, a result that Wan, Cheng, and Xu [7] improved to (ln(n − 1) + 1). Xiong, Golden, and Wasil [9] showed that the MVCA always returns a number of labels within H b of optimum, where…”

Section: The Problemmentioning

confidence: 99%

An effective genetic algorithm for the minimum-label spanning tree problem

Nummela

Julstrom

2006

Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation

View full text Add to dashboard Cite

show abstract

“…Wan, Chen, and Xu further proved that MVCA has a better performance guarantee of ln(n − 1) + 1 [13]. Xiong, Golden, and Wasil proved another bound on the worst performance of MVCA for MLST b problems, i.e., H b = b i=1 1 i , where the subscript b denotes that each label appears at most b times, and also called the maximum frequency of the labels [14].…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Evolutionary Algorithms for the Minimum Label Spanning Tree Problem

Lai

Zhou

et al. 2014

IEEE Trans. Evol. Computat.

View full text Add to dashboard Cite

Some experimental investigations have shown that evolutionary algorithms (EAs) are efficient for the minimum label spanning tree (MLST) problem. However, we know little about that in theory. As one step towards this issue, we theoretically analyze the performances of the (1+1) EA, a simple version of EAs, and a multi-objective evolutionary algorithm called GSEMO on the MLST problem. We reveal that for the MLST b problem the (1+1) EA and GSEMO achieve a b+1 2 -approximation ratio in expected polynomial times of n the number of nodes and k the number of labels. We also show that GSEMO achieves a (2ln(n))-approximation ratio for the MLST problem in expected polynomial time of n and k. At the same time, we show that the (1+1) EA and GSEMO outperform local search algorithms on three instances of the MLST problem. We also construct an instance on which GSEMO outperforms the (1+1) EA. Index TermsEvolutionary algorithm; time complexity; approximation ratio; minimum label spanning tree; multi-objective I. INTRODUCTION The minimum label spanning tree (MLST) problem is an issue arising from practice, which seeks a spanning tree with the minimum number of labels in a connected undirected graph with labeled edges. For example, we want to find a spanning tree that uses the minimum number of types of communication channels in a communication networks connected with different types of channels. The MLST problem, proposed by Chang and Leu, is proved to be NP-hard [1].For this problem, Chang and Leu have proposed two heuristic algorithms. One is the edge replacement algorithm, ERA for short, the other is the maximum vertex covering algorithm, MVCA for short. Their experimental results showed that ERA is not stable, and MVCA is more efficient.The genetic algorithm, belonging to the larger class of EAs, is a general purpose optimization algorithm [2]-[4] with a strong globally searching capacity [5]. So, Xiong, Golden, and Wasil proposed a one-parameter genetic algorithm for the MLST problem. The experimental results on extensive instances generated randomly showed that the genetic algorithm outperforms MVCA [6]. Nummela and Julstrom also proposed an efficient genetic algorithm for solving the MLST problem [7].Besides, many methods recently have been proposed for solving this NP-hard problem. Consoli et al. proposed a hybrid local search combining variable neighborhood search and simulated annealing [8]. Chwatal and Raidl presented exact methods including branch-and-cut and branch-and-cut-and-price [9]. Cerulli et al. utilized several metaheuristic methods for this problem, such as simulated annealing, reactive tabu search, the pilot method, and variable neighborhood search [10]. Consoli et al. still proposed a greedy randomized adaptive search procedure and a variable neighborhood search for solving the MLST problem [11].Since both ERA and MVCA are two original heuristic algorithms for the MLST problem, the worst performance analysis of these two algorithms, especially MVCA, is a hot research topic in recent years. Krumke ...

show abstract

“…Thus, labeled problems have been mainly studied, from a complexity and an approximability point of view, when Π is polynomial, [5,6,7,9,14,18,19]. For example, the first labeled problem introduced in the literature is the LABELED minimum spanning tree problem, which has several applications in communication network design.…”

Section: Introductionmentioning

confidence: 99%

“…For example, the first labeled problem introduced in the literature is the LABELED minimum spanning tree problem, which has several applications in communication network design. This problem is NP-hard and many complexity and approximability results have been proposed in [5,7,9,14,18,19]. On the other hand, the LABELED maximum spanning tree problem has been shown polynomial in [5].…”

Section: Introductionmentioning

confidence: 99%

The labeled perfect matching in bipartite graphs

Monnot

2005

Information Processing Letters

View full text Add to dashboard Cite

In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph G = (V, E) with |V | = 2n vertices such that E contains a perfect matching (of size n), together with a color (or label) function L : E → {c 1 , . . . , c q }, the labeled perfect matching problem consists in finding a perfect matching on G that uses a minimum or a maximum number of colors.

show abstract

Worst-case behavior of the MVCA heuristic for the minimum labeling spanning tree problem

Cited by 38 publications

References 4 publications

An effective genetic algorithm for the minimum-label spanning tree problem

An effective genetic algorithm for the minimum-label spanning tree problem

Performance Analysis of Evolutionary Algorithms for the Minimum Label Spanning Tree Problem

The labeled perfect matching in bipartite graphs

Contact Info

Product

Resources

About