Nonpolyhedral Relaxations of Graph-Bisection Problems

1995 ◽  
Vol 5 (3) ◽  
pp. 467-487 ◽  
Author(s):  
Svatopluk Poljak ◽  
Franz Rendl
Keyword(s):  
Graph Bisection

scholarly journals The peculiar phase structure of random graph bisection

2008 ◽  
Vol 49 (12) ◽  
pp. 125219 ◽  
Author(s):  
Allon G. Percus ◽  
Gabriel Istrate ◽  
Bruno Gonçalves ◽  
Robert Z. Sumi ◽  
Stefan Boettcher
Keyword(s):  
Random Graph ◽  
Phase Structure ◽  
Graph Bisection

LP-based Genetic Algorithm for the Minimum Graph Bisection Problem

2006 ◽  
pp. 315-320
Author(s):  
Michael Armbruster ◽  
Marzena Fügenschuh ◽  
Christoph Helmberg ◽  
Nikolay Jetchev ◽  
Alexander Martin
Keyword(s):  
Genetic Algorithm ◽  
Graph Bisection

GRAPH BISECTION MODELED AS CARDINALITY CONSTRAINED BINARY QUADRATIC TASK ALLOCATION

2013 ◽  
Vol 12 (02) ◽  
pp. 261-276 ◽  
Author(s):  
MARK LEWIS ◽  
GARY KOCHENBERGER
Keyword(s):  
Task Allocation ◽  
Graph Partitioning ◽  
State Of The Art ◽  
Quadratic Model ◽  
Complete Problem ◽  
Binary Model ◽  
Comparison Results ◽  
Graph Bisection ◽  
Strategic Oscillation ◽  
Np Complete

In this paper, the cardinality constrained quadratic model for binary quadratic programming is used to model and solve the graph bisection problem as well as its generalization in the form of the task allocation problem with two processors (2-TAP). Balanced graph bisection is an NP-complete problem which partitions a set of nodes in the graph G = (N, E) into two sets with equal cardinality such that a minimal sum of edge weights exists between the nodes in the two separate sets. 2-TAP is graph bisection with the addition of node preference costs in the objective function. We transform the general linear k-TAP model to the cardinality constrained quadratic binary model so that it may be efficiently solved using tabu search with strategic oscillation. On a set of benchmark graph bisections, we improve the best known solution for several problems. Comparison results with the state-of-the-art graph partitioning program METIS, as well as Cplex and Gurobi are presented on a set of randomly generated graphs. This approach is shown to also work well with 2-TAP, comparing favorably to Cplex and Gurobi, providing better solutions in a much shorter time.

scholarly journals LP and SDP branch-and-cut algorithms for the minimum graph bisection problem: a computational comparison

2012 ◽  
Vol 4 (3) ◽  
pp. 275-306 ◽  
Author(s):  
Michael Armbruster ◽  
Marzena Fügenschuh ◽  
Christoph Helmberg ◽  
Alexander Martin
Keyword(s):  
Branch And Cut ◽  
Graph Bisection ◽  
Computational Comparison

Graph bisection algorithms with good average case behavior

COMBINATORICA ◽  
1987 ◽  
Vol 7 (2) ◽  
pp. 171-191 ◽  
Author(s):  
T. N. Bui ◽  
S. Chaudhuri ◽  
F. T. Leighton ◽  
M. Sipser
Keyword(s):  
Average Case ◽  
Graph Bisection
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