# hw13 - G represent an undirected graph Also let SPATH = a G...

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CS 341: Foundations of Computer Science II Prof. Marvin Nakayama Homework 13 1. The Set Partition Problem takes as input a set S of numbers. The question is whether the numbers can be partitioned into two sets A and A = S A such that s x A x = s x A x. Show that SET-PARTITION is NP-Complete. (Hint: Reduce SUBSET-SUM .) 2. Let DOUBLE-SAT = { a φ A | φ is a Boolean formula with two satisfying assignments } . Show that DOUBLE-SAT is NP-Complete. (Hint: Reduce 3SAT .) 3. Let
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Unformatted text preview: G represent an undirected graph. Also let SPATH = { a G, a, b, k A | G contains a simple path of length at most k from a to b } and LPATH = { a G, a, b, k A | G contains a simple path of length at least k from a to b } . (a) Show that SPATH ∈ P. (b) Show that LPATH is NP-Complete. You may assume the NP-completeness of UHAMPATH , the Hamiltonian path problem for undirected graphs. 1...
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