In this paper, we consider the problem of analysing the shape of an object defined by polynomial equations in a domain. We describe regularity criteria which allow us to determine...
We study problems of reconguration of shortest paths in graphs. We prove that the shortest reconguration sequence can be exponential in the size of the graph and that it is NP-hard...
Let S Rk+m be a compact semi-algebraic set defined by P1 0, . . . , P 0, where Pi R[X1, . . . , Xk, Y1, . . . , Ym], and deg(Pi) 2, 1 i . Let denote the standard projection f...
Suppose you ran a chess tournament, everybody played everybody, and you wanted to use the results to rank everybody. Unless you were really lucky, the results would not be acyclic...
Locating a facility is often modeled as either the maxisum or the minisum problem, reflecting whether the facility is undesirable (obnoxious) or desirable. But many facilities are ...