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On the computational complexity of periodic scheduling

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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

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

Optimizing over the Growing Spectrahedron

Martin Jaggi

We devise a framework for computing an approximate solution path for an important class of parameterized semidefinite problems that is guaranteed to be ε-close to the exact solution path. The problem of computing the entire regularization path for matrix f ...

Springer Berlin Heidelberg2012

Tight Approximation Algorithms for Scheduling with Fixed Jobs and Nonavailability

Ola Nils Anders Svensson, Klaus Jansen

We study two closely related problems in nonpreemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in both cases, the objecti ...

Assoc Computing Machinery2012

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 th ...

ACM2011

Partitioned real-time scheduling on heterogeneous shared-memory multiprocessors

Martin Niemeier

We consider several real-time scheduling problems on heterogeneous multiprocessor platforms, in which the different processors share a common memory pool. These include (i)~scheduling a collection of implicit-deadline sporadic tasks with the objective of m ...

2011

Complexity of the critical node problem over trees

Marco Di Summa

In this paper we deal with the critical node problem (CNP), i.e., the problem of searching for a given number K of nodes in a graph G, whose removal minimizes the (weighted or unweighted) number of connections between pairs of nodes in the residual graph. ...

2011

Hardness of Approximating Flow and Job Shop Scheduling Problems

Ola Nils Anders Svensson

We consider several variants of the job shop problem that is a fundamental and classical problem in scheduling. The currently best approximation algorithms have worse than logarithmic performance guarantee, but the only previously known inapproximability r ...

2011

Hardness Of Precedence Constrained Scheduling On Identical Machines

Ola Nils Anders Svensson

In 1966, Graham showed that a simple procedure called list scheduling yields a 2-approximation algorithm for the central problem of scheduling precedence constrained jobs on identical machines to minimize makespan. To date this has remained the best algori ...

2011

Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut

Ola Nils Anders Svensson

We consider the Minimum Linear Arrangement problem and the (Uniform) Sparsest Cut problem. So far, these two notorious NP-hard graph problems have resisted all attempts to prove inapproximability results. We show that they have no polynomial time approxima ...

Society for Industrial and Applied Mathematics2011