{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW10 - Fall Semester 2008 CS300 Algorithms Homework#10(due...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fall Semester 2008 CS300 Algorithms Homework #10 (due 12/12) 1. The clique problem is defined as follows: Given a graph G and a positive integer k , does G have k pairwise adjacent vertices? (A set of k pairwise adjacent vertices is called a k-clique, i.e., an induced subgraph which is a complete graph K n .) Show that the clique problem is NP-complete. Hint. Use the following polynomial transformation to reduce the satisfiability problem to the clique problem. Suppose that C 1 ,C 2 , ··· C p are the clauses in a CNF expression and let the variables in the expression be denoted by x i , 1 ≤ i ≤ n . We refer to either a variable or its negation as a literal. The expression is transformed to the graph with V = { < σ,i > | σ is a literal in clause C i } , i.e., V has a vertex representing each occurrence of a literal in a clause, and E = { ( < σ,i >,< δ,j > ) | i 6 = j and σ 6 = δ } ....
View Full Document

{[ snackBarMessage ]}

Page1 / 2

HW10 - Fall Semester 2008 CS300 Algorithms Homework#10(due...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online