Labeled Traveling Salesman Problems: Complexity and approximation

Couëtoux, Basile; Gourvès, Laurent; Monnot, Jérôme; Telelis, Orestis

doi:10.1016/j.disopt.2010.02.003

Cited by 11 publications

(5 citation statements)

References 16 publications

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“…We then set the corresponding variables to 0, which allows us to reduce the instance size. In line 2, the initial subproblem is obtained (6) and (7) as well as the integrality constraints (12), (13), and (14).…”

Section: Branch-and-cut Algorithmmentioning

confidence: 99%

“…These authors proved that the problem is NP-hard and since then it has been studied by numerous researchers [3,6,9,11,12,24,31]. Many other colored problems have been studied in the literature, like the Colorful Traveling Salesman Problem [5,14,23,28,32], the Minimum Labeling Steiner Problem [7,10,13], the Labeled Maximum Matching Problem [4], the Minimum Reload Cost Cycle Cover [18], general colored problems [20], rainbow graph structures problems [25], label optimization problems [21,22,27], reload optimization problems [19,15], and some other cycle cover problems [1,2,17]. Li and Zhang [26] investigated the complexity of the rainbow tree, cycle and path partition problems and proved that identifying a RCC with the minimum number of cycles is NP-hard.…”

Section: Introduction and Problem Descriptionmentioning

confidence: 99%

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The Rainbow Cycle Cover Problem

2016

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We model and solve the Rainbow Cycle Cover Problem (RCCP). Given a connected and undirected graph G = ( V , E , L ) and a coloring function ℓ that assigns a color to each edge of G from the finite color set L , a cycle whose edges have all different colors is called a rainbow cycle. The RCCP consists of finding the minimum number of disjoint rainbow cycles covering G . The RCCP on general graphs is known to be NP-complete. We model the RCCP as an integer linear program, we derive valid inequalities and we solve it by branch-and-cut. Computational results are reported on randomly generated instances

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Section: Branch-and-cut Algorithmmentioning

confidence: 99%

Section: Introduction and Problem Descriptionmentioning

confidence: 99%

The Rainbow Cycle Cover Problem

2016

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“…In [6], the colored traveling salesman problem is considered on the points with varying colors. The Labeled Traveling Salesman Problem [7] is defined as the problem of finding a tour on a complete graph with colored edges, aiming to maximize or minimize the number of distinct colors used.…”

Section: Introductionmentioning

confidence: 99%

Angle constrained Paths

Asaeedi

Shamaee

2023

Preprint

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The traveling salesman problem (TSP) is a well-known and most widely studied problem in combinatorial optimization. The Dubins TSP is a variant of TSP for curvature-constrained vehicles. In this paper, another variant of TSP, called angle-constrained TSP, is considered for vehicles that can either move straight or turn, i.e., no voluntary curve is possible. The vehicles are only allowed to make on-the-spot turns and straight motions. We impose turn angle constraint on vehicles. Hence, some additional arbitrary points, called stop points, are added to reach an unreachable target. Here, computing the minimum number of stop points walking on the optimal TSP path is presented as the solution of angle-constrained TSP. In addition, we consider two other problems: computing an angle-constrained path on the vertices with the minimum number of stop points and computing an angle-constrained path with the minimum perimeter. In both problems, there is no need to stay on the optimal TSP path. Here, some algorithms are developed to solve these three problems and are examined on some datasets. These algorithms can be used for the path planning of robots with turn angle constraints.

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“…Besides the Label s-t Cut problem, there are still many classic optimization problems that have been considered under the edge-classified model, such as the Min Label Spanning Tree problem [5,18], the Min Label s-t Path problem [4,13], the Min Label Traveling Salesman problem [9,24], the Min Label Perfect Matching problem [19], and the Min Label Steiner Tree problem [7], etc.…”

Section: Introductionmentioning

confidence: 99%

Minimum Label s-t Cut has large integrality gaps

Zhang

Tang

2020

Information and Computation

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Given a graph G = (V, E) with a label set L = { 1 , 2 , . . . , q }, in which each edge has a label from L, a source s ∈ V , and a sink t ∈ V , the Min Label s-t Cut problem asks to pick a set L ⊆ L of labels with minimized cardinality, such that the removal of all edges with labels in L from G disconnects s and t. This problem comes from many applications in real world, for example, information security and computer networks. In this paper, we study two linear programs for Min Label s-t Cut, proving that both of them have large integrality gaps, namely, Ω(m) and Ω(m 1/3− ) for the respective linear programs, where m is the number of edges in the graph and > 0 is any arbitrarily small constant. As Min Label s-t Cut is NP-hard and the linear programming technique is a main approach to design approximation algorithms, our results give negative answer to the hope that designs better approximation algorithms for Min Label s-t Cut that purely rely on linear programming.

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Labeled Traveling Salesman Problems: Complexity and approximation

Cited by 11 publications

References 16 publications

The Rainbow Cycle Cover Problem

The Rainbow Cycle Cover Problem

Angle constrained Paths

Minimum Label s-t Cut has large integrality gaps

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