Approximate tradeoffs on weighted labeled matroids

Gourvès, Laurent; Monnot, Jérôme; Tlilane, Lydia

doi:10.1016/j.dam.2014.11.005

Cited by 4 publications

(4 citation statements)

References 36 publications

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“…In the same article, the authors give an approximation of two other multi-objective problems: max sat and cut-complement. In [9], the 1/3-approximation presented in [8] has been generalized to a bi-objective problem on simple matroids.…”

Section: Related Workmentioning

confidence: 99%

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Bi-objective matchings with the triangle inequality

Gourvès¹,

Monnot²,

Pascual³

et al. 2017

Theoretical Computer Science

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This article deals with a bi-objective matching problem. The input is a complete graph and two values on each edge (a weight and a length) which satisfy the triangle inequality. It is unlikely that every instance admits a matching with maximum weight and maximum length at the same time. Therefore, we look for a compromise solution, i.e. a matching that simultaneously approximates the best weight and the best length. For which approximation ratio ρ can we guarantee that any instance admits a ρ-approximate matching? We propose a general method which relies on the existence of an approximate matching in any graph of small size. An algorithm for computing a 1/3-approximate matching in any instance is provided. The algorithm uses an analytical result stating that every instance on at most 6 nodes must admit a 1/2-approximate matching. We extend our analysis with a computer-aided approach for larger graphs, indicating that the general method may produce a 2/5-approximate matching. We conjecture that a 1/2-approximate matching exists in any bi-objective instance satisfying the triangle inequality.

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Section: Related Workmentioning

confidence: 99%

“…If(11) holds then M = {(1, 2),(3,4)}. Finally, if neither(9) nor(11) hold then both(10) and(12)must be true and we have M = {(1, 3), (2, 4)}. Case n = 5.…”

mentioning

confidence: 98%

Bi-objective matchings with the triangle inequality

Gourvès¹,

Monnot²,

Pascual³

et al. 2017

Theoretical Computer Science

Self Cite

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“…Although computing a minimum spanning tree in the single-objective setting is polynomial-time solvable, it appears to be NP-hard for both multi-dimensional optimality concepts. Similar problems are also studied in computation social choice, where the objective is to find one spanning tree such that the satisfaction of the least satisfied agent gets maximized under different "satisfaction" notions (Darmann 2016;Darmann, Klamler, and Pferschy 2009;Escoffier, Gourvès, and Monnot 2013;Gourvès, Monnot, and Tlilane 2015). The key difference between the existing research and our work is that we are not targeting a spanning tree; instead, we are allowed to select a spanning subgraph and aim to please all agents with a minimum number of edges.…”

Section: Introductionmentioning

confidence: 99%

Multiagent MST Cover: Pleasing All Optimally via a Simple Voting Rule

et al. 2023

AAAI

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Given a connected graph on whose edges we can build roads to connect the nodes, a number of agents hold possibly different perspectives on which edges should be selected by assigning different edge weights. Our task is to build a minimum number of roads so that every agent has a spanning tree in the built subgraph whose weight is the same as a minimum spanning tree in the original graph. We first show that this problem is NP-hard and does not admit better than ((1-o(1)) ln k)-approximation polynomial-time algorithms unless P = NP, where k is the number of agents. We then give a simple voting algorithm with an optimal approximation ratio. Moreover, our algorithm only needs to access the agents' rankings on the edges. Finally, we extend our problem to submodular objective functions and Matroid rank constraints.

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“…The problem is defined as in Definition 1.1. Label s-t Cut has attracted much attention from researchers in computer science (see, e.g., [2,4,6,9,12,13,14,15]) and researchers even in chemical engineering (see [10]). The problem finds many applications in image segmentation [19], network connectivity [29], computational biology [22], and network security [1], etc.…”

Section: Introductionmentioning

confidence: 99%

Approximating the Weighted Minimum Label $s$-$t$ Cut Problem

Zhang

2020

Preprint

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In the weighted (minimum) Label s-t Cut problem, we are given a (directed or undirected) graph G = (V, E), a label set L = {ℓ 1 , ℓ 2 , . . . , ℓ q } with positive label weights {w ℓ }, a source s ∈ V and a sink t ∈ V . Each edge edge e of G has a label ℓ(e) from L. Different edges may have the same label. The problem asks to find a minimum weight label subset L ′ such that the removal of all edges with labels in L ′ disconnects s and t.The unweighted Label s-t Cut problem (i.e., every label has a unit weight) can be approximated within O(n 2/3 ), where n is the number of vertices of graph G. However, it is unknown for a long time how to approximate the weighted Label s-t Cut problem within o(n). In this paper, we provide an approximation algorithm for the weighted Label s-t Cut problem with ratio O(n 2/3 ). The key point of the algorithm is a mechanism to interpret label weight on an edge as both its length and capacity.

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Approximate tradeoffs on weighted labeled matroids

Cited by 4 publications

References 36 publications

Bi-objective matchings with the triangle inequality

Bi-objective matchings with the triangle inequality

Multiagent MST Cover: Pleasing All Optimally via a Simple Voting Rule

Approximating the Weighted Minimum Label $s$-$t$ Cut Problem

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