 
Summary: COMPLEXITY: Exercise No. 5
due in two weeks
1. (Test 99)A graph G = (V; E) has bandwidth k, if there is a bijection f : V ! f1; 2; : : : ; jV jg
such that jf(i) f(j)j k for each edge (i; j) 2 E.
a. Give a polynomial time algorithm that given a graph G with bandwidth 5 and an
appropriate mapping f , it nds a maximum independent set in G.
b. Prove or disprove: The Independent Set problem is NPcomplete on graphs with bandwidth
p
jV j.
2. (Test 99)Is the following problem NPcomplete? strongly NPcomplete?
Instance: Nonnegative integers a 1 ; a 2 ; : : : ; a 2n
Question: Is there a set S f1; 2; : : : ; 2ng such that jSj = n and
P
i2S
a i =
P
i =
2S a i ?
3. (Test 97)
