hw1(5) - CS 473G: Combinatorial Algorithms, Fall 2005...

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 DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CS 473G: Combinatorial Algorithms, Fall 2005 Homework 1 Due Tuesday, September 13, 2005, by midnight (11:59:59pm CDT) Name: Net ID: Alias: Name: Net ID: Alias: Name: Net ID: Alias: Starting with Homework 1, homeworks may be done in teams of up to three people. Each team turns in just one solution, and every member of a team gets the same grade. Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above. Staple this sheet to the top of your answer to problem 1. There are two steps required to prove NP-completeness: (1) Prove that the problem is in NP, by describing a polynomial-time verification algorithm. (2) Prove that the problem is NP-hard, by describing a polynomial-time reduction from some other NP-hard problem. Showing that the reduction is correct requires proving an if-and-only-if statement; dont forget to prove both the if part and the only if part. Required Problems 1. Some NP-Complete problems (a) Show that the problem of deciding whether one graph is a subgraph of another is NP- complete. (b) Given a boolean circuit that embeds in the plane so that no 2 wires cross, PlanarCir- cuitSat is the problem of determining if there is a boolean assignment to the inputs that makes the circuit output true. Prove that PlanarCircuitSat is NP-Complete. (c) Given a set S with 3 n numbers, 3partition is the problem of determining if S can be partitioned into n disjoint subsets, each with 3 elements, so that every subset sums to the same value. Given a set S and a collection of three element subsets of S , X3M (or exact 3-dimensional matching ) is the problem of determining whether there is a subcollection of n disjoint triples that exactly cover S ....
View Full Document

This note was uploaded on 10/14/2011 for the course ECON 101 taught by Professor Smith during the Spring '11 term at West Virginia University Institute of Technology.

Page1 / 4

hw1(5) - CS 473G: Combinatorial Algorithms, Fall 2005...

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

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