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Mathematical Programming

, Volume 90, Issue 2, pp 273–290 | Cite as

Optimization via enumeration: a new algorithm for the Max Cut Problem

  • Anna Galluccio
  • Martin Loebl
  • Jan Vondrák

Abstract.

We present a polynomial time algorithm to find the maximum weight of an edge-cut in graphs embeddable on an arbitrary orientable surface, with integral weights bounded in the absolute value by a polynomial of the size of the graph.</

The algorithm has been implemented for toroidal grids using modular arithmetics and the generalized nested dissection method. The applications in statistical physics are discussed.

Key words: cut – generating function – Pfaffian orientation – modular arithmetics 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Anna Galluccio
    • 1
  • Martin Loebl
    • 2
  • Jan Vondrák
    • 2
  1. 1.Istituto di Analisi dei Sistemi ed Informatica – CNR, viale Manzoni 30, 00185 Roma, Italy, email: galluccio@iasi.rm.cnr.itIT
  2. 2.Department of Applied Mathematics, Charles University, Malostránske nám. 25, 11800 Praha, Czech Republic, email: {loebl,vondrak}@kam.ms.mff.cuni.czCZ

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