This paper presents a fair decentralized mutual exclusion algorithm for distributed systems in which processes communicate by asynchronous message passing. The algorithm requires between N-1 and 2(N-1) messages per critical section access, where N is the number of processes in the system. The exact message complexity can be expressed as a deterministic function of concurrency in the computation. The algorithm does not introduce any other overheads over Lamport's and Ricart-Agrawala's algorithms, which require 3(N-1) and 2(N-1) messages, respectively, per critical section access and are the only other decentralized algorithms that allow mutual exclusion access in the order of the timestamps of requests.

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A fair distributed mutual exclusion algorithm

In mobile computing systems the network configuration changes due to node mobility. The paper identifies the issues a group communication service has to take into account in order to handle node mobility. These include the need to identify the location of a node, and the ability to cope with inaccuracies in the determination of a group membership. A multi level architecture for group communication in mobile systems is presented. This architecture contains a synchronous proximity layer protocol to determine the set of mobile nodes in the proximity of a given node in the network. This information is used by a three round group membership protocol for construction of groups used by mobile applications. As an example, the architecture is specialized to solve the channel allocation problem.

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Architecture for group communication in mobile systems

The basic idea of our new approach is to determine in a first step for each node those pairs of nodes which allow a good interpolation of the unknowns located at this node. These pairs of neighbor nodes (in some cases only one node) are called parent nodes. This is done by solving a local minimization problem which, in addition, yields the interpolation and restriction coefficients. The construction scheme has been generalized to systems of convection-diffusion-reaction equations using a point-block approach. After these suitable pairs of parent nodes have been determined, the nodes are labeled as C- and F-nodes such that each F-node can be interpolated using one of these suitable pairs of parent nodes and the already computed coefficients. Additionally, a simple heuristic algorithm tries to minimize the number of C-nodes and the number of non-zero entries in the coarse grid matrix. The algorithm has been parallelized and shows mesh size independent convergence for standard model problems. Realistic numerical experiments confirm the efficiency of the presented algorithm.

An O ( n 2 ) self-stabilizing algorithm for computing bridge-connected components

The maximum subarray problem (MSP) involves selection of a segment of consecutive array elements that has the largest possible sum over all other segments in a given array. The efficient algorithms for the MSP and related problems are expected to contribute to various applications in genomic sequence analysis, data mining or in computer vision etc. The MSP is a conceptually simple problem, and several linear time optimal algorithms for 1D version of the problem are already known. For 2D version, the currently known upper bounds are cubic or near-cubic time. For the wider applications, it would be interesting if multiple maximum subarrays are computed instead of just one, which motivates the work in the first half of the thesis. The generalized problem of K-maximum subarray involves finding K segments of the largest sum in sorted order. Two subcategories of the problem can be defined, which are K-overlapping maximum subarray problem (K-OMSP), and K-disjoint maximum subarray problem (K-DMSP). Studies on the K-OMSP have not been undertaken previously, hence the thesis explores various techniques to speed up the computation, and several new algorithms. The first algorithm for the 1D problem is of O(Kn) time, and increasingly efficient algorithms of O(K + n logK) time, O((n+K) logK) time and O(n+K logmin(K,n)) time are presented. Considerations on extending these results to higher dimensions are made, which contributes to establishing O(n) time for 2D version of the problem where K is bounded by a certain range. Ruzzo and Tompa studied the problem of all maximal scoring subsequences, whose definition is almost identical to that of the K-DMSP with a few subtle differences. Despite slight differences, their linear time algorithm is readily capable of computing the 1D K-DMSP, but it is not easily extended to higher dimensions. This observation motivates a new algorithm based on the tournament data structure, which is of O(n+K logmin(K,n)) worst-case time. The extended version of the new algorithm is capable of processing a 2D problem in O(n + min(K,n) · n logmin(K,n)) time, that is O(n) for K ≤ n log n . For the 2D MSP, the cubic time sequential computation is still expensive for practical purposes considering potential applications in computer vision and data mining. The second half of the thesis investigates a speed-up option through parallel computation. Previous parallel algorithms for the 2D MSP have huge demand for hardware resources, or their target parallel computation models are in the realm of pure theoretics. A nice compromise between speed and cost can be realized through utilizing a mesh topology. Two mesh algorithms for the 2D MSP with O(n) running time that require a network of size O(n) are designed and analyzed, and various techniques are considered to maximize the practicality to their full potential.

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Sequential and Parallel Algorithms for the Generalized Maximum Subarray Problem

Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for real-time optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the best-possible approximation to the minimum-weight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimum-weight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained sequentially to that of the solution computed in parallel can be arbitrarily large.

Parallel real-time optimization: beyond speedup

1. Introduction and Background 2. Models of Parallel Computation 3. Complexity of Parallel Algorithms 4. Merging and Sorting 5. Selection and Searching 6. Matrix Computations 7. Algorithms for Unweighted Graphs 8. Algorithms for Weighted Graphs 9. Updating Algorithms for Graphs

Pranay Chaudhuri

Papers

Parallel algorithms: design and analysis

Distributed computing: Optimal algorithm for mutual exclusion in mesh-connected computer networks

Distributed processing of graphs: fundamental cycles algorithm