A possible winner of an election is a candidate that has, in some kind of incomplete-information election, the possibility to win in a complete extension of the election. The first type of problem we study is the Possible co-Winner with respect to the Addition of New Candidates (PcWNA) problem, which asks, given an election with strict preferences over the candidates, is it possible to make a d...

In the monograph “Axioms and Hulls” (1992) [2] Donald Knuth studies some axiomatizations of geometric situations. The structures described by one of the axiom systems are called CC-systems. Knuth proves that it is NP-complete to decide, whether a partially defined CC-system can be extended to a complete CC-system. The aim of this note is to show that Knuth’s proof of this result also implies th...

The parameterized computational complexity of a collection of well-known problems including: Bandwidth, Precedence constrained k-processor scheduling, Longest Common Subsequence, DNA physical mapping (or Intervalizing colored graphs), Perfect phylogeny (or Triangulating colored graphs), Colored cutwidth, and Feasible register assignment is explored. It is shown that these problems are hard for ...

The eeect of query order on NP-completeness is investigated. A sequence ~ D = (D 1 ; : : : ; D k) of decision problems is deened to be sequentially complete for NP if each D i 2 NP and every problem in NP can be decided in polynomial time with one query to each of D 1 ; : : : ; D k in this order. It is shown that, if NP contains a language that is p-generic in the sense of Ambos-Spies, Fleischh...

A graph is a tree of paths (cycles), if its vertex set can be partitioned into clusters, such that each cluster induces a simple path (cycle), and the clusters form a tree. Our main result states that the problem whether or not a given graph is a tree of paths (cycles) is NP-complete. Moreover, if the length of the paths (cycles) is bounded by a constant, the problem is in P.

The aim of edge modification problems is to change the edge set of a given graph as little as possible in order to satisfy a certain property. Edge modification problems in graphs have a lot of applications in different areas, and many polynomial-time algorithms and NP-completeness proofs for this kind of problems are known. In this work we prove new NP-completeness results for these problems i...

We discuss the problem of finding a simple polygonalization for a given set of vertices P that has optimal area. We show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P and prove that it is NP-complete to find a minimum weight polygon or a maximum weight polygon for a given vertex set, resulting in a ...

We consider some problems about pairs of disjoint NP sets. The theory of these sets with a natural concept of reducibility is, on the one hand, closely related to the theory of proof systems for propositional calculus, and, on the other, it resembles the theory of NP completeness. Furthermore, such pairs are important in cryptography. Among others, we prove that the Broken Mosquito Screen pair ...

This paper provides a logical analysis of the problem of version space maintenance which highlights fundamental differences between version spaces of boolean concepts and version spaces for structural descriptions. It then employs the theory of NP-completeness in a heuristic manner to isolate a variety of respects in which the standard version space maintenance procedure is intractable in the c...

Let K be an infinite field. We give polynomial time constructions of families of r-dimensional subspaces of Kn with the following transversality property: any linear subspace of Kn of dimension n− r is transversal to at least one element of the family. We also give a new NP-completeness proof for the following problem: given two integers n and m with n m and a n ×m matrix A with entries in Z, d...