We study the Minimum Circuit Size Problem (MCSP): given the truth-table of a Boolean function f and a number k, does there exist a Boolean circuit of size at most k computing f? This is a fundamental NP problem that is not known to be NP-complete. Previous work has studied consequences of the NP-completeness of MCSP. We extend this work and consider whether MCSP may be complete for NP under mor...

In integer programming, {0, 1/2}-cuts are Gomory–Chvátal cuts that can be derived from the original linear system by using coefficients of value 0 or 1/2 only. The separation problem for {0, 1/2}-cuts is strongly NP-hard. We show that separation remains strongly NP-hard, even when all integer variables are binary. © 2011 Elsevier B.V. All rights reserved.

We show the NP-Completeness of two processor scheduling with tasks of execution time 1 or 2 units and unit interprocessor communication latency. We develop a model of scheduling in the presence of communication contention, and show the NP-Completeness of two processor scheduling with unit execution time tasks in our model.

Flexible flow shop scheduling problem (FFS) with unrelated parallel machines contains sequencing in flow shop where, at any stage, there exists one or more processors. The objective consists of minimizing the maximum completion time. Because of NP-completeness of FFS problem, it is necessary to use heuristics method to address problems of moderate to large scale problem. Therefore, for assessme...

TETRAVEX is a widely played one person computer game in which you are given n2 unit tiles, each edge of which is labelled with a number. The objective is to place each tile within a n by n square such that all neighbouring edges are labelled with an identical number. Unfortunately, playing TETRAVEX is computationally hard. More precisely, we prove that deciding if there is a tiling of the TETRA...

Kaboozle is a puzzle consisting of several square cards, each annotated with colored paths and dots drawn on both sides and holes drilled. The goal is to join two colored dots with paths of the same color (and fill all holes) by stacking the cards suitably. The freedoms here are to reflect, rotate, and order the cards arbitrarily, so it is not surprising that the problem is NP-complete (as we s...

In the nineties Immerman and Medina initiated the search for syn- tactic tools to prove NP-completeness. In their work, amongst several results, they conjecture that the NP-completeness of a problem defined by the conjunction of a sentence in Existential Second Order Logic with a First Order sentence, necessarily imply the NP-completeness of the problem defined by the Existential Second Order s...

Of course, the even more general problem where the pattern is a graph is already well-known to be NP-complete, as it contains the well-known NP-complete Subgraph Isomorphism problem as the special case k = 1. We thus see here that restricting to tree patterns does not lower the worst-case complexity. The NP-completeness of Disjoint Occurrences of T3 follows immediately from the NP-completeness ...