The problem of determining whether two given finite graphs are isomorphic is easily seen to belong to the class NP. But up to now, no polynomial time algorithm is known. On the other hand, no NP-completeness proof is known either. That is, GRAPH ISOMORPHISM is one of the few “open problems” in NP according to Garey and Johnson’s terminology [9]. Note that GRAPH ISOMORPHISM is already mentioned ...

A salesman in a red suit who looks suspiciously like Tom Waits presents you with a black steel box with n binary switches on the front and a light bulb on the top. The salesman tells you that the state of the light bulb is controlled by a complex boolean circuit—a collection of AND, OR, and NOT gates connected by wires, with one input wire for each switch and a single output wire for the light ...

A salesman in a red suit who looks suspiciously like Tom Waits presents you with a black steel box with n binary switches on the front and a light bulb on the top. The salesman tells you that the state of the light bulb is controlled by a complex boolean circuit—a collection of AND, OR, and NOT gates connected by wires, with one input wire for each switch and a single output wire for the light ...

For any fixed parameter k ≥ 1, a tree k–spanner of a graph G is a spanning tree T in G such that the distance between every pair of vertices in T is at most k times their distance in G. In this paper, we generalize on this very restrictive concept, and introduce Steiner tree k–spanners: We are given an input graph consisting of terminals and Steiner vertices, and we are now looking for a tree k...

The known facts about solvability of equations over groups are considered from a more general point of view. A generalized version of the theorem about solvability of unimodular equations over torsion-free groups is proved. In a special case, this generalized version become a multivariable variant of this theorem. For unimodular (ordinary and generalized) equations over torsion free groups, we ...

Consider a graph G, in which the set of vertices represents the set of demand points as well as the set of potential facility sites. The classical covering location problem seeks to minimize the total location cost required to cover all vertices of G. The conditional covering problem (CCP) has the same objective but with an additional constraint: each selected facility site must be covered by a...

We consider a geometric set covering problem. In its original form it consists of adding stations to an existing geometric transportation network so that each of a given set of settlements is not too far from a station. The problem is known to be NP-hard in general. However, special cases with certain properties have been shown to be efficiently solvable in theory and in practice, especially if...

This paper presents two solution methodologies for the Visual Area Coverage Scheduling problem. The objective is to schedule a number of dynamic observers over a given 3D terrain such that the total visual area covered (viewed) over a planning horizon is maximal. This problem is a more complicated extension of the Set Covering Problem, known to be Np-Hard. We present two decomposition based heu...

Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a) are measurable in both time and one spatial variable, and VMO in the other spatial variables. The coefficient a is measurable in time and VMO in the spatial variables. The unique solvability of equations in the whole space is applied to solving Dirichlet and oblique derivative pr...

A graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of th...