Reoptimization of the metric deadline TSP

Böckenhauer, Hans-Joachim; Komm, Dennis

doi:10.1016/j.jda.2009.04.001

Cited by 24 publications

(24 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since then, many other optimization problems were discussed in this setting, including Steiner tree [7,10,11,18], minimum spanning tree [14], as well as various versions of tsp [4,9,12]. In all cases, the goal is to propose reoptimization algorithm that outperform their deterministic counterparts in terms of complexity and/or approximation ratio.…”

Section: Introductionmentioning

confidence: 99%

Reoptimization of maximum weight induced hereditary subgraph problems

Boria

Monnot

Paschos

2013

Theoretical Computer Science

View full text Add to dashboard Cite

The reoptimization issue studied in this paper can be described as follows: given an instance I of some problem Π, an optimal solution OPT for Π in I and an instance I ′ resulting from a local perturbation of I that consists of insertions or removals of a small number of data, we wish to use OPT in order to solve Π in I ′ , either optimally or by guaranteeing an approximation ratio better than that guaranteed by an ex nihilo computation and with running time better that that needed for such a computation. We use this setting in order to study weighted versions of several representatives of a broad class of problems known in the literature as maximum induced hereditary subgraph problems. The main problems studied are max independent set, max k-colorable subgraph, max P k -free subgraph, max split subgraph and max planar subgraph. We also show, how the techniques presented allow us to handle also bin packing.

show abstract

Section: Introductionmentioning

confidence: 99%

Reoptimization of maximum weight induced hereditary subgraph problems

Boria

Monnot

Paschos

2013

Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

“…Since then, reoptimization has been applied to various problems like the TSP [4][5][6][7], the Steiner tree problem [8][9][10][11], the shortest common superstring problem [12,13], the knapsack problem [14], and several covering problems [15].…”

Section: Overview Of Reoptimization Resultsmentioning

confidence: 99%

Knowing All Optimal Solutions Does Not Help for TSP Reoptimization

Böckenhauer

Hromkovič

Sprock

2011

Computation, Cooperation, and Life

Self Cite

View full text Add to dashboard Cite

“…Some approximation results on reoptimization can be found in [2,3,4,6]. In [9], one can find an overview on reoptimization. Let us consider the reoptimization problem of ∆HPP 2 , where the modification is to change one of the end vertices.…”

Section: Related Known Resultsmentioning

confidence: 99%

Structural Properties of Hard Metric TSP Inputs

Mömke

2011

SOFSEM 2011: Theory and Practice of Computer Science

View full text Add to dashboard Cite

The metric traveling salesman problem is one of the most prominent APX-complete optimization problems. An important particularity of this problem is that there is a large gap between the known upper bound and lower bound on the approximability (assuming P = N P ). In fact, despite more than 30 years of research, no one could find a better approximation algorithm than the 1.5-approximation provided by Christofides. The situation is similar for a related problem, the metric Hamiltonian path problem, where the start and the end of the path are prespecified: the best approximation ratio up to date is 5/3 by an algorithm presented by Hoogeveen almost 20 years ago.In this paper, we provide a tight analysis of the combined outcome of both algorithms. This analysis reveals that the sets of the hardest input instances of both problems are disjoint in the sense that any input is guaranteed to allow at least one of the two algorithms to achieve a significantly improved approximation ratio. In particular, we show that any input instance that leads to a 5/3-approximation with Hoogeveen's algorithm enables us to find an optimal solution for the traveling salesman problem. This way, we determine a set S of possible pairs of approximation ratios. Furthermore, for any input we can identify one pair of approximation ratios within S that forms an upper bound on the achieved approximation ratios.

show abstract

Reoptimization of the metric deadline TSP

Cited by 24 publications

References 21 publications

Reoptimization of maximum weight induced hereditary subgraph problems

Reoptimization of maximum weight induced hereditary subgraph problems

Knowing All Optimal Solutions Does Not Help for TSP Reoptimization

Structural Properties of Hard Metric TSP Inputs

Contact Info

Product

Resources

About