Robust Assignments via Ear Decompositions and Randomized Rounding

Adjiashvili, David; Bindewald, Viktor; Michaels, Dennis

doi:10.4230/lipics.icalp.2016.71

Cited by 3 publications

(6 citation statements)

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“…[25,1] for thorough literature reviews on the topic). The Bulk-Robust framework was introduced by Adjiashvili, Stiller and Zenklusen [6] and later studied further in [4,17,2,8]. Robustness with respect to the cost structure of the problem represents another important avenue of research.…”

Section: Additional Related Workmentioning

confidence: 99%

Flexible Graph Connectivity: Approximating Network Design Problems Between 1- and 2-connectivity

Adjiashvili,

Hommelsheim,

Mühlenthaler

2019

Preprint

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Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation problem (WTAP) are all examples of fundamental well-studied network design tasks that postulate different initial states of the network and different assumptions on the reliability of network components. In this paper we motivate and study Flexible Graph Connectivity (FGC), a problem that mixes together both the modeling power and the complexities of all aforementioned problems and more. In a nutshell, FGC asks to design a connected network, while allowing to specify different reliability levels for individual edges. While this non-uniform nature of the problem makes it appealing from the modeling perspective, it also renders most existing algorithmic tools for dealing with network design problems unfit for approximating FGC.In this paper we develop a general algorithmic approach for approximating FGC that yields approximation algorithms with ratios that are very close to the best known bounds for many special cases, such as 2-ECSS and WTAP. Our algorithm and analysis combine various techniques including a weight-scaling algorithm, a charging argument that uses a variant of exchange bijections between spanning trees and a factor revealing non-linear optimization problem. * This is a preliminary version and will be updated soon.

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Section: Additional Related Workmentioning

confidence: 99%

Flexible Graph Connectivity: Approximating Network Design Problems Between 1- and 2-connectivity

Adjiashvili,

Hommelsheim,

Mühlenthaler

2019

Preprint

Self Cite

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“…However, due to our inapproximability result for Weighted Robust Matching Augmentation, this can not be true, unless NP ⊆ ZTIME(n polylog(n) ). The authors of [2] agree that their analysis is incorrect.…”

Section: Introductionmentioning

confidence: 96%

“…Robust matching augmentation can be stated also as a design problem, where the given infrastructure is available at zero cost and the host graph is a complete bipartite graph. In fact, our problem is a special case of the bulkrobust assignment problem, a design problem introduced in [2]. Bulk-robustness is a redundancy-based robustness concept proposed by Adjiashvili, Stiller and Zenklusen [3], which allows to specify a list of failure scenarios.…”

Section: Introductionmentioning

confidence: 99%

“…Bulk-robustness is a redundancy-based robustness concept proposed by Adjiashvili, Stiller and Zenklusen [3], which allows to specify a list of failure scenarios. The bulk-robust assignment problem is known to be NP-hard even if only one of two fixed edges may fail [2]. Here we consider the setting that any single edge may fail.…”

Section: Introductionmentioning

confidence: 99%

“…Related work Adjiashvili, Bindewald and Michaels in [2] proposed an LPbased randomized algorithm for the bulk-robust assignment problem. They claim an O(log n)-factor approximation guarantee for their algorithm.…”

Section: Introductionmentioning

confidence: 99%

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How to Secure Matchings Against Edge Failures

Hommelsheim¹,

Mühlenthaler²,

Schaudt³

2018

Preprint

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Suppose we are given a bipartite graph that admits a perfect matching and an adversary may delete any edge from the graph with the intention of destroying all perfect matchings. We consider the task of adding a minimum cost edge-set to the graph, such that the adversary never wins. We provide efficient exact and approximation algorithms. In particular, for the unit-cost problem, we provide a log 2 n-factor approximation algorithm and a polynomial-time algorithm for chordal-bipartite graphs. Furthermore, we give a fixed parameter algorithm for the problem parameterized by the treewidth of the input graph. For general non-negative weights we settle the approximability of the problem and show a close relation to the Directed Steiner Forest Problem. Additionally we prove a dichotomy theorem characterizing minor-closed graph classes which allow for a polynomial-time algorithm. Our methods rely on a close relationship to the classical strong connectivity augmentation problem and directed Steiner problems.

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Robust combinatorial optimization under convex and discrete cost uncertainty

Buchheim

Kurtz

2018

EURO Journal on Computational Optimization

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Robust Assignments via Ear Decompositions and Randomized Rounding

Cited by 3 publications

References 0 publications

Flexible Graph Connectivity: Approximating Network Design Problems Between 1- and 2-connectivity

Flexible Graph Connectivity: Approximating Network Design Problems Between 1- and 2-connectivity

How to Secure Matchings Against Edge Failures

Robust combinatorial optimization under convex and discrete cost uncertainty

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