Tight Lower Bounds for Certain Parameterized NP-Hard Problems

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) mO(1) , 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, hitting set, set cover, and feature set, cannot be solved in time no(k) mO(1) , 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, independent set, and dominatin...

• Type: Conference
• Year: 2004
• Where: COCO
• Authors: Jianer Chen, Benny Chor, Mike Fellows, Xiuzhen Huang, David W. Juedes, Iyad A. Kanj, Ge Xia
• Keywords: Algorithms, COCO 2004, NP-hard Problems, Parameterized Problems, Parameterized Weighted Satisfiability