The problem of parametric scheduling in hard real-time systems, (in the presence of linear relative constraints between the start and execution times of tasks) was posed in Sak94] and GPS95]. In GPS95], a polynomial time algorithm is presented for the case when the constraints are restricted to be standard (deened in x6) and the execution time vectors… (More)
It is well-known that the Vertex Cover problem is in P on bipartite graphs, however; the computational complexity of the Partial Vertex Cover problem on bipartite graphs is open. In this paper, we first show that the Partial Vertex Cover problem is NP-hard on bipartite graphs. We then identify an interesting special case of bipartite graphs, for which the… (More)
In this paper, we propose an efficient method for implementing Dijkstra's algorithm for the Single Source Shortest Path Problem (SSSPP) in a graph with positively lengthed edges, and where there are few distinct lengths. The SSSPP is one of the most widely studied problems in theoretical computer science and operations research. On a graph with n vertices,… (More)
We consider the satisfiability problem for Boolean combinations of unit two variable per inequality (UTVPI) constraints. A UTVPI constraint is linear constraint containing at most two variables with non-zero coefficients, where furthermore those coefficients must be either −1 or 1. We prove that if a satisfying solution exists, then there is a solution with… (More)
In this article, we exploit the graphical structure of 2SAT formulas to show that the shortest tree-like resolution refutation of an unsatisfiable 2SAT formula can be determined in polynomial time.