A distributed shortest path algorithm for a planar network

AbstractAn algorithm is presented for finding a single source shortest path tree in a planar undirected distributed network with nonnegative edge costs. The number of messages used by the algorithm is O(n53) on an n-node network. Distributed algorithms are also presented for finding a breath-first spanning tree in general network, for finding a shortest path tree in a general network, for finding a separator of a planar network, and for finding a division of a planar network

Parallel implementations of dynamic traffic assignment models and algorithms for dynamic shortest path problems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2004.Includes bibliographical references (p. 139-144).This thesis aims at the development of faster Dynamic Traffic Assignment (DTA) models to meet the computational efficiency required by real world applications. A DTA model can be decomposed into several sub-models, of which the most time consuming ones are the dynamic network loading model and the user's route choice model. We apply parallel computing technology to the dynamic network loading model to achieve faster implementations. To the best of our knowledge, this concerns the first parallel implementations of macroscopic DTA models. Two loading algorithms are studied: the iterative loading algorithm and the chronological loading algorithm. For the iterative loading algorithm, two parallelization strategies are implemented: decomposition by network topology and by time. For the chronological loading algorithm, the network topology decomposition strategy is implemented. Computational tests are carried out in a distributed-memory environment. Satisfactory speedups are achieved. We design efficient shortest path algorithms to speedup the user's route choice model. We first present a framework for static shortest path algorithms, which prioritize nodes with optimal distance labels in the scan eligible list. Then we apply the framework in dynamic FIFO, strict FIFO, and static networks. Computational tests show significant speedups. We proceed to present two other shortest path algorithms: Algorithm Delta and Algorithm Hierarchy. We also provide the evaluations of the algorithms.by Hai Jiang.S.M

High Performance Software Reconfiguration in the Context of Distributed Systems and Interconnection Networks.

Designed algorithms that are useful for developing protocols and supporting tools for fault tolerance, dynamic load balancing, and distributing monitoring in loosely coupled multi-processor systems. Four efficient algorithms are developed to learn network topology and reconfigure distributed application programs in execution using the available tools for replication and process migration. The first algorithm provides techniques for transparent software reconfiguration based on process migration in the context of quadtree embeddings in Hypercubes. Our novel approach provides efficient reconfiguration for some classes of faults that may be identified easily. We provide a theoretical characterization to use graph matching, quadratic assignment, and a variety of branch and bound techniques to recover from general faults at run-time and maintain load balance. The second algorithm provides distributed recognition of articulation points, biconnected components, and bridges. Since the removal of an articulation point disconnects the network, knowledge about it may be used for selective replication. We have obtained the most efficient distributed algorithms with linear message complexity for the recognition of these properties. The third algorithm is an optimal linear message complexity distributed solution for recognizing graph planarity which is one of the most celebrated problems in graph theory and algorithm design. Recently, efficient shortest path algorithms are developed for planar graphs whose efficient recognition itself was left open. Our algorithm also leads to designing efficient distributed algorithm to recognize outer-planar graphs with applications in Hamiltonian path, shortest path routing and graph coloring. It is shown that efficient routing of information and distributing the stack needed for for planarity testing permit local computations leading to an efficient distributed algorithm. The fourth algorithm provides software redundancy techniques to provide fault tolerance to program structures. We consider the problem of mapping replicated program structures to provide efficient communication between modules in multiple replicas. We have obtained an optimal mapping of 2-replicated binary trees into hypercubes. For replication numbers greater than two, we provide efficient heuristic simulation results to provide efficient support for both \u27N-version programming\u27 and \u27Recovery block\u27 approaches for software replication

Effective algorithms and protocols for wireless networking: a topological approach

Much research has been done on wireless sensor networks. However, most protocols and algorithms for such networks are based on the ideal model Unit Disk Graph (UDG) model or do not assume any model. Furthermore, many results assume the knowledge of location information of the network. In practice, sensor networks often deviate from the UDG model significantly. It is not uncommon to observe stable long links that are more than five times longer than unstable short links in real wireless networks. A more general network model, the quasi unit-disk graph (quasi-UDG) model, captures much better the characteristics of wireless networks. However, the understanding of the properties of general quasi-UDGs has been very limited, which is impeding the design of key network protocols and algorithms. In this dissertation we study the properties for general wireless sensor networks and develop new topological/geometrical techniques for wireless sensor networking. We assume neither the ideal UDG model nor the location information of the nodes. Instead we work on the more general quasi-UDG model and focus on figuring out the relationship between the geometrical properties and the topological properties of wireless sensor networks. Based on such relationships we develop algorithms that can compute useful substructures (planar subnetworks, boundaries, etc.). We also present direct applications of the properties and substructures we constructed including routing, data storage, topology discovery, etc. We prove that wireless networks based on quasi-UDG model exhibit nice properties like separabilities, existences of constant stretch backbones, etc. We develop efficient algorithms that can obtain relatively dense planar subnetworks for wireless sensor networks. We also present efficient routing protocols and balanced data storage scheme that supports ranged queries. We present algorithmic results that can also be applied to other fields (e.g., information management). Based on divide and conquer and improved color coding technique, we develop algorithms for path, matching and packing problem that significantly improve previous best algorithms. We prove that it is unlikely for certain problems in operation science and information management to have any relatively effective algorithm or approximation algorithm for them