The complexity of designing a network with minimum diameter | Zendy

Plesnik J. | Zendy

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The complexity of designing a network with minimum diameter

Author(s) -

Plesnik J.

Publication year - 1981

Publication title -

networks

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.977

H-Index - 64

eISSN - 1097-0037

pISSN - 0028-3045

DOI - 10.1002/net.3230110110

Subject(s) - combinatorics , mathematics , graph , enhanced data rates for gsm evolution , constraint (computer aided design) , simple graph , planar graph , simple (philosophy) , mathematical optimization , computer science , discrete mathematics , artificial intelligence , geometry , philosophy , epistemology

Given a graph G with edge lengths and costs, we wish to find a subgraph F of G which connects up all the original vertices and minimizes the maximum distance in F , subject to a budget constraint on the sum of the edge costs. In this note we establish NP‐hardness for the design problem, even for the simple case where G is a planar graph with maximum degree 3 and the budget restricts the choice to spanning trees. Moreover, the problem of finding a near optimal subgraph F is also NP‐hard.

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