Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Limits on Interconnection Network Performance
IEEE Transactions on Parallel and Distributed Systems
Optimal Algorithms for Broadcast and Gossip in the Edge-Disjoint Path Modes (Extended Abstract)
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
A new look at fault tolerant network routing
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Analysis of Chordal Ring Network
IEEE Transactions on Computers
Eigenvalues and graph bisection: An average-case analysis
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Graph Bisection Algorithins With Good Average Case Behavior
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Simulated annealing for graph bisection
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Lower bounds for the partitioning of graphs
IBM Journal of Research and Development
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An edge-bisector of a graph is a set of edges whose removing separates the graph into two subgraphs of same order, within one. The edge-bisection of a graph is the cardinality of the smallest edge-bisector. The main purpose of this paper is to estimate the quality of general bounds on the edge-bisection of Cayley graphs. For this purpose we have focused on chordal rings of degree 3. These graphs are Cayley graphs on the dihedral group and can be considered as the simplest Cayley graphs on a non-abelian group (the dihedral group is metabelian). Moreover, the natural plane tessellation used to represent and manipulate these graphs can be generalized to other types of tessellations including abelian Cayley graphs. We have improved previous bounds on the edge-bisection of chordal rings and we have shown that, for any fixed chord, our upper bound on the edge-bisection of chordal rings is optimal up to an O(log n) factor. Finally, we have given tight bounds for optimal chordal rings, that are those with the maximum number of vertices for a given diameter.