April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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Tractable and Non-tractable Problems 473
Thus the case of n = 4 (or more) and 2 colours is trivial for an algorithm to answer the question “Given
a map, can we colour it with n colours only?’’
The case of three colours is really interesting, as it is in NPC.
The graphs having n nodes, each connected with all the remaining, clearly require n colours. Such a
graph is called a clique.
The problem for graph colouring states “Find the minimum number of colours required to colour a given
graph.” The problem is in NPC. The corresponding Yes/No problem, “Can we colour the given graph with k
colours, where k is also given?’’, is also in NPC.
17.3.4 What is a Certifi cate?
All the above mentioned problems require that the algorithm trying to solve them, ...
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