General troubleshooting is NP-hard

Extensions of Decision-Theoretic Troubleshooting: Cost Clusters and Precedence Constraints

In decision-theoretic troubleshooting [5,2], we try to find a cost efficient repair strategy for a malfunctioning device described by a formal model. The need to schedule repair actions under uncertainty has required the researchers to use an appropriate knowledge representation formalism, often a probabilistic one. The troubleshooting problem has received considerable attention over the past t...

Tenacity and some other Parameters of Interval Graphs can be computed in polynomial time

In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two different vulnerability parameters of graphs, tenacity and rupture degree are defined. In general, computing the tenacity o...

Parallelizing Assignment Problem with DNA Strands

Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...

Troubleshooting: NP-hardness and solution methods

Packing Segments in a Convex 3-Polytope is NP-hard

We show it is NP-hard to pack the maximum number of segments in a convex 3-dimensional polytope. We show this packing problem is also NP-hard for general polygonal regions in the plane. This problem relates two streams of research, Kakeya set problems and packing problems.