Tight lower bounds for certain parameterized NP-hard problems Conference Paper uri icon

abstract

  • Based on the framework of parameterized complexity theory, we derive tight lower bounds on the computational complexity for a number of well-known NP-hard problems. We start by proving a general result, namely that the parameterized weighted satisfiability problem on depth-t circuits cannot be solved in time no(k)poly(m), where n is the circuit input length, m is the circuit size, and k is the parameter, unless the (t - 1)-st level W[t - 1] of the W-hierarchy collapses to FPT. By refining this technique, we prove that a group of parameterized NP-hard problems, including WEIGHTED SAT, DOMINATING SET, HITTING SET, SET COVER, and FEATURE SET, cannot be solved in time n o(k) poly(m), where n is the size of the universal set from which the k elements are to be selected and m is the instance size, unless the first level W[1] of the W-hierarchy collapses to FPT. We also prove that another group of parameterized problems which includes WEIGHTED q-SAT (for any fixed q 2), CLIQUE, and INDEPENDENT SET, cannot be solved in time no(k) unless all search problems in the syntactic class SNP, introduced by Papadimitriou and Yannakakis, are solvable in subexponential time. Note that all these parameterized problems have trivial algorithms of running time either nk poly (m) or O(nk).

name of conference

  • 19th Annual IEEE Conference on Computational Complexity (CCC 2004), 21-24 June 2004, Amherst, MA, USA

published proceedings

  • 19TH IEEE ANNUAL CONFERENCE ON COMPUTATIONAL COMPLEXITY, PROCEEDINGS

author list (cited authors)

  • Chen, J., Chor, B., Fellows, M., Huang, X. Z., Juedes, D., Kanj, I., & Xia, G.

complete list of authors

  • Chen, J||Chor, B||Fellows, M||Huang, XZ||Juedes, D||Kanj, I||Xia, G

publication date

  • October 2004