Webbläsaren som du använder stöds inte av denna webbplats. Alla versioner av Internet Explorer stöds inte längre, av oss eller Microsoft (läs mer här: * https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Var god och använd en modern webbläsare för att ta del av denna webbplats, som t.ex. nyaste versioner av Edge, Chrome, Firefox eller Safari osv.

Subexponential-time algorithms for maximum independent set and related problems on box graphs

Författare

Summary, in English

A box graph is the intersection graph of orthogonal rectangles in the plane. We consider such basic combinatorial problems on box graphs as maximum independent set, minimum vertex cover and maximum induced subgraph with polynomial-time testable hereditary property Pi. We show that they can be exactly solved in subexponential time, more precisely, in time 2(O(rootnlog n)), by applying Miller's simple cycle planar separator theorem [6] (in spite of the fact that the input box graph might be strongly non-planar). Furthermore we extend our idea to include the intersection graphs of orthogonal d-cubes of bounded aspect ratio and dimension. We present an algorithm that solves maximum independent set and the other aforementioned problems in time 2(O(d2dbn1-1/dlogn)) on, such box graphs in d-dimensions. We do this by applying a separator theorem by Smith and Wormald [7]. Finally, we show that in general graph case substantially subexponential algorithms for maximum independent set and the maximum induced subgraph with polynomial-time testable hereditary property Pi problems can yield non-trivial upper bounds on approximation factors achievable in polynomial time.

Avdelning/ar

  • Computer Science

Publiceringsår

2003

Språk

Engelska

Sidor

50-56

Publikation/Tidskrift/Serie

Computing and combinatorics / Lecture notes in computer science

Volym

2697

Dokumenttyp

Konferensbidrag

Förlag

Springer

Ämne

  • Computer Science

Conference name

9th Annual International Conference, COCOON 2003

Conference date

2003-07-25 - 2003-07-28

Conference place

Big Sky, MT, United States

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0302-9743
  • ISSN: 1611-3349
  • ISBN: 978-3-540-40534-4