The impact of the growth rate of the packing number of graphs on the computational complexity of the independent set problem
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D. S. Malyshev
Abstract
We study the dependence of complexity of the independent set problem depending on the asymptotic growth of the packing number of graphs (as a function of the number of vertices). It is shown that under some natural assumptions this problem is solvable in polynomial time if and only if the order of growth of the packing number is not than higher the logarithm of the number of vertices.
This work was supported by the Russian Foundation for Basic Research, project No. 10- 01-00357-a, 11-01-00107-a, and 12-01-00749-a, the Federal Target Programme “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” for 2009-2012 (state contract No. 16.740.11.0310 and 14.B37.21.0393), and the Laboratory of Algorithms and Technologies for Networks Analysis at the National Research University “Higher School of Economics” (a grant of the Government of the Russian Federation, contract no. 11.G34.31.0057).
© 2014 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- Distance-regular graph with the intersection array {45, 30, 7; 1, 2, 27} does not exist
- The impact of the growth rate of the packing number of graphs on the computational complexity of the independent set problem
- Traveling salesman polytopes and cut polytopes. Affine reducibility
- Minors of the constraint matrix in multi-index transport problems
- Cycle structure of power mappings in a residue classes ring
- A criterion for the automata realizable functions to be boundedly deterministic
- On the complexity of two-dimensional discrete logarithm problem in a finite cyclic group with effective automorphism of order
- The completeness criterion for some systems containing P-sets of automaton functions
- On the synthesis of circuits admitting complete fault detection test sets of constant length under arbitrary constant faults at the outputs of the gates
- Factorially solvable rings
- Identities with permutations and quasigroups isotopic to groups and to Abelian groups
- Classes of projectively equivalent quadrics over local rings
