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Approximating ATSP by Relaxing Connectivity

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Strengths and Limitations of Linear Programming Relaxations

Abbas Bazzi

Many of the currently best-known approximation algorithms for NP-hard optimization problems are based on Linear Programming (LP) and Semi-definite Programming (SDP) relaxations. Given its power, this class of algorithms seems to contain the most favourable ...

EPFL2017

We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor approximation was give ...

Springer Int Publishing Ag2016

The vehicle routing problem with cross-dock selection is a variant of the vehicle routing problem containing spatial and load synchronization constraints by which products are transferred and processed via at least one cross-dock. This paper presents a mat ...

Pergamon-Elsevier Science Ltd2016

, ,

We consider the capacitated -center problem. In this problem we are given a finite set of locations in a metric space and each location has an associated non-negative integer capacity. The goal is to choose (open) locations (called centers) and assign each ...

Springer Heidelberg2015

No Small Linear Program Approximates Vertex Cover within a Factor 2 - e

Ola Nils Anders Svensson, Abbas Bazzi

The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regevproved that the problem is NP-hard to approximate within a factor2 - ∈, assuming the Unique Games Conjecture (UGC). This is tig ...

IEEE Computer Society2015

Improving Christofides' Algorithm for the s-t Path TSP

Hyung Chan An

We present a deterministic (1+root 5/2)-approximation algorithm for the s-t path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian path between the t ...

Assoc Computing Machinery2015

The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ_1

Nisheeth Vishnoi

In this article, we disprove a conjecture of Goemans and Linial; namely, that every negative type metric embeds into ℓ1 with constant distortion. We show that for an arbitrarily small constant δ > 0, for all large enough n, there is an n-point negative ...

Association for Computing Machinery2015

Node-weighted network design and maximum sub-determinants

Carsten Moldenhauer

We consider the Node-weighted Steiner Forest problem on planar graphs. Demaine et al. showed that a generic primal-dual algorithm gives a 6-approximation. We present two different proofs of an approximation factor of~

3

. Then, we draw a connection to Goem ...

EPFL2014

Centrality of Trees for Capacitated k-Center

Ola Nils Anders Svensson, Hyung Chan An, Aditya Bhaskara

We consider the capacitated k-center problem. In this problem we are given a finite set of locations in a metric space and each location has an associated non-negative integer capacity. The goal is to choose (open) k locations (called centers) and assign e ...

Springer2014

Approximation algorithms for regret minimization in vehicle routing problems

Adrian Aloysius Bock

In this thesis, we present new approximation algorithms as well as hardness of approximation results for NP-hard vehicle routing problems related to public transportation. We consider two different problem classes that also occur frequently in areas such a ...

EPFL2014

Node-weighted network design and maximum sub-determinants

Carsten Moldenhauer

3

. Then, we draw a connection to Goem ...

EPFL2014