Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Mathematical Programming: Series A and B
Fast approximation algorithms for multicommodity flow problems
Selected papers of the 23rd annual ACM symposium on Theory of computing
A branch-and-cut algorithm for the equicut problem
Mathematical Programming: Series A and B
The node capacitated graph partitioning problem: a computational study
Mathematical Programming: Series A and B - Special issue on computational integer programming
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
Progress Made in Solving the Multicommodity Flow Problem
SIAM Journal on Optimization
Solving Graph Bisection Problems with Semidefinite Programming
INFORMS Journal on Computing
On the Bisection Width and Expansion of Butterfly Networks
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Computer Networks: The International Journal of Computer and Telecommunications Networking
Better bounds for graph bisection
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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In this paper new and generalized lower bounds for the graph partitioning problem are presented. These bounds base on the well known lower bound of embedding a clique into the given graph with minimal congestion. This is equivalent to a multicommodity flow problem where each vertex sends a commodity of size one to every other vertex. Our new bounds use arbitrary multicommodity flow instances for the bound calculation, the critical point for the lower bound is the guaranteed cut flow of the instances. Furthermore, a branch&bound procedure basing on these bounds is presented and finally it is shown that the new bounds are also useful for lower bounds on classes of graphs, e.g. the Butterfly and Bene?s graph.