Domination Reliability
Klaus Dohmen, Peter Tittmann
TL;DR
This paper introduces a new network reliability measure called domination reliability, relating it to graph polynomials and hypergraph coverage, with explicit formulas and complexity analysis.
Contribution
It defines domination reliability, connects it to existing graph concepts, derives formulas, and proves NP-hardness of computation.
Findings
Derived explicit and recursive formulas for domination reliability.
Established an analogue of Whitney's broken circuit theorem.
Proved that computing domination reliability is NP-hard.
Abstract
We propose a new network reliability measure for some particular kind of service networks, which we refer to as domination reliability. We relate this new reliability measure to the domination polynomial of a graph and the coverage probability of a hypergraph. We derive explicit and recursive formulae for domination reliability and its associated domination reliability polynomial, deduce an analogue of Whitney's broken circuit theorem, and prove that computing domination reliability is NP-hard.
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Taxonomy
TopicsEconomic Policies and Impacts · Game Theory and Voting Systems