A self-stabilizing interval routing scheme in general networks

The Pivot Interval Routing (PIR) scheme [EGP98] divides the nodes in the network into pivots and clients of the pivots. A pivot acts as a center for the partition of the network formed by its clients. Each node can send messages directly only to a small subset of vertices in its nearby vicinity or to the pivots; An algorithm is called self-stabilizing [Dij74] if, starting from an arbitrary initial state, it is guaranteed to reach a correct state in finite time and with no exterior help. In this thesis, we present a self-stabilizing PIR algorithm. The algorithm starts with no knowledge of the network architecture and, eventually, each node builds its own routing table of size O(n1/2log3/2 n + Deltaupsilon, log n) bits with a total of O(n3/2 log3/2 n) bits. The stabilization time of the algorithm is O&parl0;dn1+logn &parr0; time units, where n is the number of nodes and d is the diameter of the network. (Abstract shortened by UMI.)

Distributed stabilizing data structures

Distributed algorithms aim to achieve better performance than sequential algorithms in terms of time complexity (or asymptotic time complexity) while keeping or lowering the memory requirement (space complexity) in a node. (In sequential algorithms, the memory requirement is the memory requirement of the algorithm itself.); Self-stabilizing distributed algorithms aim to achieve a comparable performance to non-stabilizing distributed algorithms when transient faults or arbitrary initialization cause the system to enter a state where a non-stabilizing algorithm cannot continue to properly perform its task; Transient faults can affect an existing data structure and alter its data content. As a result, the data structure may lose its properties, and the operations defined over the data structure will have unpredictable and undesirable results, making the data structure unusable; We present several self or snap-stabilizing algorithms for particular data structures; We propose an optimal self-stabilizing distributed algorithm for simultaneously activating non-adjacent processes on an oriented chain (Algorithm SSDS ). We use Algorithm SSDS to accomplish two tasks: local mutual exclusion and line sorting. We propose two uniform, self-stabilizing, deterministic protocols on oriented chains: a time and space optimal solution to the local mutual exclusion problem (Algorithm LMEC ), and a space and (asymptotic) time optimal solution to the distributed sorting problem (Algorithm SORTc ); We extend Algorithm SSDS to an asynchronous oriented ring with a distinguished node with some minor modifications, and we obtain general self-stabilization for simultaneously activated non-adjacent processes in an oriented ring with a distinguished process (Algorithm SSDSR ). We use Algorithm SSDSR to accomplish two tasks: local resource allocation and ring sorting. We propose two uniform, self-stabilizing, deterministic protocols on oriented rings: a time and space optimal solution to the local resource allocation problem (Algorithm LRAR ), and a space and (asymptotic) time optimal solution to the distributed sorting problem (Algorithm SORTr ); We extend Algorithm SSDS to an asynchronous rooted tree, and we obtain general self-stabilization for simultaneously activated non-adjacent processes in a rooted tree (Algorithm SSDST ). We then give two applications of Algorithm SSDST : a time and space optimal solution to the local mutual exclusion problem (Algorithm LMET ) and a space and (asymptotically) time optimal solution to the min heap problem (Algorithm HEAP ); In proving the time complexity of sorting, we introduce the notion of pseudo-time, similar to logical time introduced by Lamport; We present the first snap-stabilizing distributed binary search tree (BST) algorithm. The proposed algorithm uses a heap algorithm (Algorithm Heap) as a preprocessing step. This is also the first snap-stabilizing distributed solution to the heap problem

Abstract

We study the coverage problem from the fault tolerance point of view for sensor networks. Fault tolerance is a critical issue for sensors deployed in places where they are not easily replaceable, repairable and rechargeable. The failure of one node should not incapacitate the entire network. We propose three 1-fault tolerant models, and we compare them to each other, as well as with the minimal coverage model [11]. To study the reliability of proposed models, we develop the Markov model for each of them and calculate the reliability assuming a constant failure rate. We show that the most unreliable model among these three models is the hexagonal model, and the improved model is the most reliable on long term. For short time from the start, the square model is more reliable, but after a short while, the improved model becomes and remains the better one

Optimal Embedding of Honeycomb networks into Hypercubes

We present an optimal embedding of a honeycomb network (honeycomb mesh and honeycomb torus) of size n into a hypercube with expansion ratio of when n is a power of two. When n is not a power of two, the expansion is , which we conjecture to be near optimal. For a honeycomb mesh, the dilation of the embedding is 1. For a honeycomb torus, the dilation can be as large as 2⌈log n⌉+3, because of the extra links connecting symmetric opposite nodes of degree two. A honeycomb network, built recursively using hexagon tessellation, is a multiprocessor interconnection network, and also a Cayley graph, and it is better than the planar mesh with the same number of nodes in terms of degree, diameter, number of links, and bisection width