April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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Some NP and NP-Complete Problems 519
18.4.8 Independent Set
Defi nition If G = (V, E) and V′ ⊆ V, then V′ is an independent set iff no two nodes in V′ are connected by
an edge in E.
Problem IS
Input G = (V, E), k ∈ N, k ≤ |V |
Question Does G have an independent set of size k?
An equivalent question is Does G have an independent set of size at least k?
Related problems
ISS
1
: Given a graph, fi nd the size of a largest independent set.
ISS
2
: Given a graph, fi nd a largest independent set.
Note ISS
1
p
→
IS. Try k = n, k = n – 1, . . . until we get a Yes answer. This is a P-time linear search.
Claim IS is in NPC.
Proof First we show that IS ∈ NP.
1. ...
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