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CS 373: Combinatorial Algorithms, Spring 2001
http://wwwcourses.cs.uiuc.edu/~cs373
Homework 6 (due Tue. May 1, 2001 at 11:59.99 p.m.)
Name:
Net ID:
Alias:
U
3
/
4
1
Name:
Net ID:
Alias:
U
3
/
4
1
Name:
Net ID:
Alias:
U
3
/
4
1
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. Since 1unit graduate
students are required to solve problems that are worth extra credit for other students,
1unit grad
students may not be on the same team as 3/4unit grad students or undergraduates.
Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above.
Please also tell us whether you are an undergraduate, 3/4unit grad student, or 1unit grad student
by circling U,
3
/
4
, or 1, respectively. Staple this sheet to the top of your homework.
Note:
You will be held accountable for the appropriate responses for answers (e.g. give models,
proofs, analyses, etc). For NPcomplete problems you should prove everything rigorously, i.e. for
showing that it is in NP, give a description of a certi±cate and a poly time algorithm to verify it,
and for showing NPhardness, you must show that your reduction is polytime (by similarly proving
something about the algorithm that does the transformation) and proving both directions of the
‘if and only if’ (a solution of one is a solution of the other) of the manyone reduction.
Required Problems
1. Complexity
(a) Prove that P
⊆
coNP.
(b) Show that if NP
n
= coNP, then
every
NPcomplete problem is
not
a member of coNP.
2. 2CNFSAT
Prove that deciding satis±ability when all clauses have at most 2 literals is in P.
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