On reducing the complexity of matrix clocks

Matrix clocks are a generalization of the notion of vector clocks that allows the local representation of causal precedence to reach into an asynchronous distributed computation's past with depth $x$, where $x\ge 1$ is an integer. Maintaining matrix clocks correctly in a system of $n$ nodes requires that everymessage be accompanied by $O(n^x)$ numbers, which reflects an exponential dependency of the complexity of matrix clocks upon the desired depth $x$. We introduce a novel type of matrix clock, one that requires only $nx$ numbers to be attached to each message while maintaining what for many applications may be the most significant portion of the information that the original matrix clock carries. In order to illustrate the new clock's applicability, we demonstrate its use in the monitoring of certain resource-sharing computations

A distributed transportation simplex applied to a Content Distribution Network problem

A Content Distribution Network (CDN) can be defined as an overlay system that replicates copies of contents at multiple points of a network, close to the final users, with the objective of improving data access. CDN technology is widely used for the distribution of large-sized contents, like in video streaming. In this paper we address the problem of finding the best server for each customer request in CDNs, in order to minimize the overall cost. We consider the problem as a transportation problem and a distributed algorithm is proposed to solve it. The algorithm is composed of two independent phases: a distributed heuristic finds an initial solution that may be later improved by a distributed transportation simplex algorithm. It is compared with the sequential version of the transportation simplex and with an auction-based distributed algorithm. Computational experiments carried out on a set of instances adapted from the literature revealed that our distributed approach has a performance similar or better to its sequential counterpart, in spite of not requiring global information about the contents requests. Moreover, the results also showed that the new method outperforms the based-auction distributed algorithm

A distributed transportation simplex applied to a Content Distribution Network problem

A Content Distribution Network (CDN) can be defined as an overlay system that replicates copies of contents at multiple points of a network, close to the final users, with the objective of improving data access. CDN technology is widely used for the distribution of large-sized contents, like in video streaming. In this paper we address the problem of finding the best server for each customer request in CDNs, in order to minimize the overall cost. We consider the problem as a transportation problem and a distributed algorithm is proposed to solve it. The algorithm is composed of two independent phases: a distributed heuristic finds an initial solution that may be later improved by a distributed transportation simplex algorithm. It is compared with the sequential version of the transportation simplex and with an auction-based distributed algorithm. Computational experiments carried out on a set of instances adapted from the literature revealed that our distributed approach has a performance similar or better to its sequential counterpart, in spite of not requiring global information about the contents requests. Moreover, the results also showed that the new method outperforms the based-auction distributed algorithm