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Approximability of Sparse Integer Programs

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LP-Based Algorithms for Capacitated Facility Location

Ola Nils Anders Svensson, Hyung Chan An

Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of algorithmic methodo ...

IEEE2014

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

Strong LP Formulations for Scheduling Splittable Jobs on Unrelated Machines

Ola Nils Anders Svensson

We study a natural generalization of the problem of minimizing makespan on unrelated machines in which jobs may be split into parts. The different parts of a job can be (simultaneously) processed on different machines, but each part requires a setup time b ...

Springer2014

Tracking Interacting Objects Optimally Using Integer Programming

Pascal Fua, François Fleuret, Engin Türetken, Xinchao Wang

In this paper, we show that tracking different kinds of interacting objects can be formulated as a network-flow Mixed Integer Program. This is made possible by tracking all objects simultaneously and expressing the fact that one object can appear or disapp ...

Springer Int Publishing Ag2014

Bin Packing via Discrepancy of Permutations

Friedrich Eisenbrand, Thomas Rothvoss, Doemoetoer Palvoelgyi

A well-studied special case of bin packing is the 3-partition problem, where n items of size > 1/4 have to be packed in a minimum number of bins of capacity one. The famous Karmarkar-Karp algorithm transforms a fractional solution of a suitable LP relaxati ...

Association for Computing Machinery2013

New Results in the Theory of Linear and Integer Programming

Nicolai Hähnle

The polynomial Hirsch conjecture states that the vertex-edge diameter of a d-dimensional polyhedron with n facets is bounded by a polynomial in d and n. For the special case where the polyhedron is defined as the set of points satisfying a system Ax ≤ b of ...

EPFL2012

Polynomial Approximations for Continuous Linear Programs

Daniel Kuhn

Continuous linear programs have attracted considerable interest due to their potential for modeling manufacturing, scheduling, and routing problems. While efficient simplex-type algorithms have been developed for separated continuous linear programs, crude ...

2012

Santa Claus Schedules Jobs On Unrelated Machines

Ola Nils Anders Svensson

One of the classic results in scheduling theory is the 2-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines; i.e., job j requires time p(ij) if processed on machine i. More t ...

Siam Publications2012

Primal and dual linear decision rules in stochastic and robust optimization

Daniel Kuhn, Wolfram Wiesemann

Linear stochastic programming provides a flexible toolbox for analyzing real-life decision situations, but it can become computationally cumbersome when recourse decisions are involved. The latter are usually modeled as decision rules, i.e., functions of t ...

2011

Node-weighted network design and maximum sub-determinants

Carsten Moldenhauer

3

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

EPFL2014