It is shown that the MAX2SAT problem is NP-complete even if every variable appears in at most three clauses. However, if every variable appears in at most two clauses, it is shown that it (and even the general MAXSAT problem) can be solved in linear time. When every variable appears in at most three clauses, we give an exact algorithm for MAXSAT that takes at most O(3 n=2 n) steps where n is th...

NP-complete problems should be hard on some instances but these may be extremely rare. On generic instances many such problems, especially related to random graphs, have been proven easy. We show the intractability of random instances of a graph coloring problem: this graph problem is hard on average unless all NP problem under any samplable (i.e. generateable in polynomial time) distribution a...

The system design process translates the customers’ needs into a buildable system design. It requires selecting subsystems from an allowable set and matching the interfaces between them. Designs that meet the top-level input and output requirements are tested to see how well they meet the system’s performance and cost goals. This paper proves that the System Design Problem is NP-complete by red...

The Maze Generation problem has been presented as a benchmark for the Second Answer Set Programming Competition. We prove that the problem is NP–complete and identify relevant classes of unsatisfiable instances. The Maze Generation (MG) problem has been presented as a benchmark for the Second Answer Set Programming (ASP) Competition1. The problem has been placed in the NP category, which contai...

During the last years, the genomes of more and more species have been sequenced, providing data for phylogenetic reconstruction based on genome rearrangement measures, where the most important distance measures are the reversal distance and the transposition distance. The two main tasks in all phylogenetic reconstruction algorithms is to calculate pairwise distances and to solve the median of t...

The co phylogeny reconstruction problem is that of finding minimum cost explanations of differences between historical associations. The problem arises in parasitology, molecular systematics, and biogeography. Existing software tools for this problem either have worst-case exponential time or use heuristics that do not guarantee optimal solutions. To date, no polynomial time optimal algorithms ...