In a network of asynchronous processors, the cost to send a message can diier signiicantly from one communication link to another. Assume that associated with each link is a positive weight representing the cost of sending one message along the link and the cost of an algorithm executed on a weighted network is the sum of the costs of all messages sent during its execution. We present a distrib...

Highly-optimized concurrent algorithms are often hard to prove correct because they have no natural decomposition into separately provable parts. This paper presents a proof technique for the modular verification of such non-modular algorithms. It generalizes existing verification techniques based on a totally-ordered hierarchy of refinements to allow a partiallyordered hierarchy-that is: a lat...

The minimum spanning tree (MST) is widely used in planning the most economical network. algorithm for finding MST of a connected graph essential. In this paper, new proposed based on deduced theorem MST. first sorts edges according to their weight, from large small. Next, premise ensuring connectivity graph, it deletes order until number equal vertexes minus 1. Finally, remaining an This equiva...

In this paper we consider bi-criteria geometric optimization problems, in particular, the minimum diameter minimum cost spanning tree problem and the minimum radius minimum cost spanning tree problem for a set of points in the plane. The former problem is to construct a minimum diameter spanning tree among all possible minimum cost spanning trees, while the latter is to construct a minimum radi...