Distributed Algorithm for the minimum k-center problem

Aleš Černivec (2010) Distributed Algorithm for the minimum k-center problem. MSc thesis.

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Abstract

In this thesis we present a distributed algorithm designed for peer-to-peer (P2P) networks that can efficiently solve the problem of minimum k-center. The algorithm iteratively improves the deployment of service access points and by that the quality of service (QoS) for the service clients. Algorithm autonomously adapts to changes in the network and converges towards better service deployment. By doing so, it improves the QoS for the clients in P2P networks. The main goals of our work was development of a distributed algorithm solving the facility location problem of minimum k-centers. The algorithm was applied to the problem of service deployment location in the PlanetLab globally distributed research network. In the development of the algorithm, we used a simulator for distributed algorithms PeerSim and our own communication framework DCenter. We analyzed the solutions of the new distributed algorithm by simulating the algorithm in the networks of up to 1500 nodes. We found out that the quality of solutions to these problems follow the trends of existing serial 2-approximation algorithms solving the problem of the minimum k-center. We tested the algorithm on static networks provided by the standard OR-LIB library on different values of the parameter k. It was observed that in cases of small value of k the new distributed algorithm yielded better results than the serial 2-approximative Gonzalez algorithm. We tested the algorithm on dynamic networks where we noticed that removing the nodes from the network was not the most time consuming operation (20 to 50 percent more messages). Adding the nodes introduced up to 2-times more network traffic than removing the nodes. The implementation was tested in PlanetLab research network running the algorithm in generic networks of up to 40 nodes. Networks were created using the universal network generator BRITE which was also used in the case of dynamic networks. Using the proposed distributed algorithm we have approximately solved the NP-hard minimum k-center problem. Moreover, we have shown that the usage of this algorithm would provide better user experience in the distributed environment in P2P networks by improving on the QoS in the network.

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