Designing Efficient Algorithms for Distributed Systems.

Search for efficient algorithms for distributed systems has become an important area of computer science. This research is driven by the need to efficiently process and communicate information generated by the system. In distributed systems, topological information plays an important role in the design of fast algorithms for problems such as routing, broadcasting, and sorting. The central focus of this dissertation is the design and analysis of distributed algorithms for determining topological information in asynchronous communication networks. Specifically, we present distributed algorithms for two generic problems: distributed graph problems and network traversal problems. Network location and network recognition are two important graph problems in distributed systems. We present unified algorithms for locating centers and medians of asynchronous communication networks. Also, we present both the centralized and decentralized versions of the algorithm. Furthermore, this is the first decentralized algorithm reported in the literature. These results are further extended to weighted networks. In addition, the unified algorithm can also be used to determine other topological parameters such as the diameter, and centroids of distributed networks. Efficient algorithms for problems such as finding shortest paths, centers, and sorting could be designed if the network topology is known a priori. Towards this end, we solve an open problem of recognizing mesh (grid) structures. We formulate both centralized and decentralized algorithms for recognizing mesh networks. The time and message complexities of the algorithm are O(n\sp{1.6}) and O(e+nlogn), respectively, where n is the number of nodes and e is the number of edges of the graph underlying the network. Network traversal is a fundamental activity in a distributed system and it has been widely studied in the literature. We present efficient distributed algorithms for depth first traversal of an asynchronous communication network and show the usefulness of this algorithm in deriving efficient solutions to the problems related to network learning. Finally, we discuss application of some of these algorithms in distributed sensor networks

Generalized centrality in trees

In 1982, Slater defined path subgraph analogues to the center, median, and (branch or branchweight) centroid of a tree. We define three families of central substructures of trees, including three types of central subtrees of degree at most D that yield the center, median, and centroid for D = 0 and Slater's path analogues for D = 2. We generalize these results concerning paths and include proofs that each type of generalized center and generalized centroid is unique. We also present algorithms for finding one or all generalized central substructures of each type.

Self-stabilizing tree algorithms

Designers of distributed algorithms have to contend with the problem of making the algorithms tolerant to several forms of coordination loss, primarily faulty initialization. The processes in a distributed system do not share a global memory and can only get a partial view of the global state. Transient failures in one part of the system may go unnoticed in other parts and thus cause the system to go into an illegal state. If the system were self-stabilizing, however, it is guaranteed that it will return to a legal state after a finite number of state transitions. This thesis presents and proves self-stabilizing algorithms for calculating tree metrics and for achieving mutual exclusion on a tree structured distributed system

A New Characterization of Tree Medians with Applications to Distributed Algorithms

A new characterization of tree medians is presented: we show that a vertex m is a median of a tree T with n vertices iff there exists a partition of the vertex set into [n/2] disjoint pairs (excluding m when n is odd), such that all the paths connecting the two vertices in any of the pairs pass through m. We show that in this case this sum is the largest possible among all such partitions, and we use this fact to discuss lower bounds on the message complexity of the distributed sorting problem. This lower bound implies that, given a network of a tree topology, choosing a median and then route all the information through it is the best possible strategy, in terms of worst-case number of messages sent during any execution of any distributed sorting algorithm. We also discuss the implications for networks of a general topology and for the distributed ranking problem

Coordination of Mobile Mules via Facility Location Strategies

In this paper, we study the problem of wireless sensor network (WSN) maintenance using mobile entities called mules. The mules are deployed in the area of the WSN in such a way that would minimize the time it takes them to reach a failed sensor and fix it. The mules must constantly optimize their collective deployment to account for occupied mules. The objective is to define the optimal deployment and task allocation strategy for the mules, so that the sensors' downtime and the mules' traveling distance are minimized. Our solutions are inspired by research in the field of computational geometry and the design of our algorithms is based on state of the art approximation algorithms for the classical problem of facility location. Our empirical results demonstrate how cooperation enhances the team's performance, and indicate that a combination of k-Median based deployment with closest-available task allocation provides the best results in terms of minimizing the sensors' downtime but is inefficient in terms of the mules' travel distance. A k-Centroid based deployment produces good results in both criteria.Comment: 12 pages, 6 figures, conferenc

Fast Distributed Computation of Distances in Networks

This paper presents a distributed algorithm to simultaneously compute the diameter, radius and node eccentricity in all nodes of a synchronous network. Such topological information may be useful as input to configure other algorithms. Previous approaches have been modular, progressing in sequential phases using building blocks such as BFS tree construction, thus incurring longer executions than strictly required. We present an algorithm that, by timely propagation of available estimations, achieves a faster convergence to the correct values. We show local criteria for detecting convergence in each node. The algorithm avoids the creation of BFS trees and simply manipulates sets of node ids and hop counts. For the worst scenario of variable start times, each node i with eccentricity ecc(i) can compute: the node eccentricity in diam(G)+ecc(i)+2 rounds; the diameter in 2*diam(G)+ecc(i)+2 rounds; and the radius in diam(G)+ecc(i)+2*radius(G) rounds.Comment: 12 page