You're given a simple undirected graph G with N vertices and M edges. You have to assign, to each vertex i, a number C; such that 1 ≤ C; < N and Vi‡j, C; ‡ C₁. For any such assignment, we define D; to be the number of neighbours j of i such that C; < C₁. You want to minimise maxi{[1..N) Di - minic{1..N} Di. 3 Output the minimum possible value of this expression for a valid assignment as described above, and also print the corresponding assignment. Note: • The given graph need not be connected. • If there are multiple possible assignments, output anyone. • Since the input is large, prefer using fast input-output methods.

You're given a simple undirected graph G with N vertices and M edges. You have to assign, to each vertex i, a number C; such that 1 ≤ C; < N and Vi‡j, C; ‡ C₁. For any such assignment, we define D; to be the number of neighbours j of i such that C; < C₁. You want to minimise maxi{[1..N) Di - minic{1..N} Di. 3 Output the minimum possible value of this expression for a valid assignment as described above, and also print the corresponding assignment. Note: • The given graph need not be connected. • If there are multiple possible assignments, output anyone. • Since the input is large, prefer using fast input-output methods.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter18: Deterministic Dynamic Programming

Section18.4: Resource-allocation Problems

Problem 3P

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