Algorithmic and explicit determination of the Lovász number for certain circulant graphs

Authors:
Valentin Brimkov
Affiliations:
Mathematics Department, SUNY Buffalo State College, Buffalo, NY 14222, USA
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 17
Cited 0

An analogue of the shannon capacity of a graph

SIAM Journal on Algebraic and Discrete Methods
A note on the Shannon capacity of run-length-limited codes

IEEE Transactions on Information Theory
Introduction to parallel algorithms and architectures: array, trees, hypercubes

Introduction to parallel algorithms and architectures: array, trees, hypercubes
Optimal Distance Networks of Low Degree for Parallel Computers

IEEE Transactions on Computers
Computational geometry in C

Computational geometry in C
Distributed loop computer networks: a survey

Journal of Parallel and Distributed Computing
Randomized graph products, chromatic numbers, and Lovasz j-function

STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Optimal distributed algorithms in unlabeled tori and chordal rings

Journal of Parallel and Distributed Computing
On the capacity of digraphs

European Journal of Combinatorics
A Combinatorial Problem Related to Multimodule Memory Organizations

Journal of the ACM (JACM)
Linear Programming in Linear Time When the Dimension Is Fixed

Journal of the ACM (JACM)
Semidefinite programs and association schemes

Computing - Special issue on combinatorial optimization
Recursive Diagonal Torus: An Interconnection Network for Massively Parallel Computers

IEEE Transactions on Parallel and Distributed Systems
Spirograph Theory: A Framework for Calculations on Digitized Straight Lines

IEEE Transactions on Pattern Analysis and Machine Intelligence
Codes over tori

IEEE Transactions on Information Theory
On the Shannon capacity of a graph

IEEE Transactions on Information Theory
Repeated communication and Ramsey graphs

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.04

Visualization

Abstract

We consider the problem of computing the Lovász theta function for circulant graphs Cn,J of degree four with n vertices and chord length J, 2≤J≤n. We present an algorithm that takes O(J) operations if J is an odd number, and O(n/J) operations if J is even. On the considered class of graphs our algorithm strongly outperforms the known algorithms for theta function computation. We also provide explicit formulas for the important special cases J=2 and J=3.