98 research outputs found

    Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree

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    We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of O(nlogΔ)O(n\log \Delta) bits per node and O(nD)O(nD) respectively, where Δ\Delta is the highest degree of a node, nn is the number of nodes and DD is the diameter of the network. In contrast, our algorithm has a space complexity of O(logn)O(\log n) bits per node, which is optimal for silent-stabilizing spanning trees and runs in O(n)O(n) time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, We also present a (non-sielnt) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones

    Fast and compact self-stabilizing verification, computation, and fault detection of an MST

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    This paper demonstrates the usefulness of distributed local verification of proofs, as a tool for the design of self-stabilizing algorithms.In particular, it introduces a somewhat generalized notion of distributed local proofs, and utilizes it for improving the time complexity significantly, while maintaining space optimality. As a result, we show that optimizing the memory size carries at most a small cost in terms of time, in the context of Minimum Spanning Tree (MST). That is, we present algorithms that are both time and space efficient for both constructing an MST and for verifying it.This involves several parts that may be considered contributions in themselves.First, we generalize the notion of local proofs, trading off the time complexity for memory efficiency. This adds a dimension to the study of distributed local proofs, which has been gaining attention recently. Specifically, we design a (self-stabilizing) proof labeling scheme which is memory optimal (i.e., O(logn)O(\log n) bits per node), and whose time complexity is O(log2n)O(\log ^2 n) in synchronous networks, or O(Δlog3n)O(\Delta \log ^3 n) time in asynchronous ones, where Δ\Delta is the maximum degree of nodes. This answers an open problem posed by Awerbuch and Varghese (FOCS 1991). We also show that Ω(logn)\Omega(\log n) time is necessary, even in synchronous networks. Another property is that if ff faults occurred, then, within the requireddetection time above, they are detected by some node in the O(flogn)O(f\log n) locality of each of the faults.Second, we show how to enhance a known transformer that makes input/output algorithms self-stabilizing. It now takes as input an efficient construction algorithm and an efficient self-stabilizing proof labeling scheme, and produces an efficient self-stabilizing algorithm. When used for MST, the transformer produces a memory optimal self-stabilizing algorithm, whose time complexity, namely, O(n)O(n), is significantly better even than that of previous algorithms. (The time complexity of previous MST algorithms that used Ω(log2n)\Omega(\log^2 n) memory bits per node was O(n2)O(n^2), and the time for optimal space algorithms was O(nE)O(n|E|).) Inherited from our proof labelling scheme, our self-stabilising MST construction algorithm also has the following two properties: (1) if faults occur after the construction ended, then they are detected by some nodes within O(log2n)O(\log ^2 n) time in synchronous networks, or within O(Δlog3n)O(\Delta \log ^3 n) time in asynchronous ones, and (2) if ff faults occurred, then, within the required detection time above, they are detected within the O(flogn)O(f\log n) locality of each of the faults. We also show how to improve the above two properties, at the expense of some increase in the memory

    Self-Stabilizing Token Distribution with Constant-Space for Trees

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    Self-stabilizing and silent distributed algorithms for token distribution in rooted tree networks are given. Initially, each process of a graph holds at most l tokens. Our goal is to distribute the tokens in the whole network so that every process holds exactly k tokens. In the initial configuration, the total number of tokens in the network may not be equal to nk where n is the number of processes in the network. The root process is given the ability to create a new token or remove a token from the network. We aim to minimize the convergence time, the number of token moves, and the space complexity. A self-stabilizing token distribution algorithm that converges within O(n l) asynchronous rounds and needs Theta(nh epsilon) redundant (or unnecessary) token moves is given, where epsilon = min(k,l-k) and h is the height of the tree network. Two novel ideas to reduce the number of redundant token moves are presented. One reduces the number of redundant token moves to O(nh) without any additional costs while the other reduces the number of redundant token moves to O(n), but increases the convergence time to O(nh l). All algorithms given have constant memory at each process and each link register

    Snap-Stabilization in Message-Passing Systems

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    In this paper, we tackle the open problem of snap-stabilization in message-passing systems. Snap-stabilization is a nice approach to design protocols that withstand transient faults. Compared to the well-known self-stabilizing approach, snap-stabilization guarantees that the effect of faults is contained immediately after faults cease to occur. Our contribution is twofold: we show that (1) snap-stabilization is impossible for a wide class of problems if we consider networks with finite yet unbounded channel capacity; (2) snap-stabilization becomes possible in the same setting if we assume bounded-capacity channels. We propose three snap-stabilizing protocols working in fully-connected networks. Our work opens exciting new research perspectives, as it enables the snap-stabilizing paradigm to be implemented in actual networks

    Space programs summary no. 37-63, volume 1 for the period 1 March - 30 April 1970. Flight projects

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    Mariner Mars 1971, Mariner Venus-Mercury 1973 and Viking Orbiter 1975 status report

    Distributed stabilizing data structures

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    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

    Asynchronous neighborhood task synchronization

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    Faults are likely to occur in distributed systems. The motivation for designing self-stabilizing system is to be able to automatically recover from a faulty state. As per Dijkstra\u27s definition, a system is self-stabilizing if it converges to a desired state from an arbitrary state in a finite number of steps. The paradigm of self-stabilization is considered to be the most unified approach to designing fault-tolerant systems. Any type of faults, e.g., transient, process crashes and restart, link failures and recoveries, and byzantine faults, can be handled by a self-stabilizing system; Many applications in distributed systems involve multiple phases. Solving these applications require some degree of synchronization of phases. In this thesis research, we introduce a new problem, called asynchronous neighborhood task synchronization ( NTS ). In this problem, processes execute infinite instances of tasks, where a task consists of a set of steps. There are several requirements for this problem. Simultaneous execution of steps by the neighbors is allowed only if the steps are different. Every neighborhood is synchronized in the sense that all neighboring processes execute the same instance of a task. Although the NTS problem is applicable in nonfaulty environments, it is more challenging to solve this problem considering various types of faults. In this research, we will present a self-stabilizing solution to the NTS problem. The proposed solution is space optimal, fault containing, fully localized, and fully distributed. One of the most desirable properties of our algorithm is that it works under any (including unfair) daemon. We will discuss various applications of the NTS problem

    Study of efficient transmission and reception of image-type data using millimeter waves

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    Evaluation of signal processing and modulation techniques for transmission and reception of image type data via millimeter wave relay satellite

    Space programs summary no. 37-66, volume 3 for the period 1 October - 30 November 1970. Supporting research and advanced development

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    Research studies on development of Thermoelectric Outer Planet Spacecraft /TOPS/ and lunar exploratio

    Notes on Theory of Distributed Systems

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    Notes for the Yale course CPSC 465/565 Theory of Distributed Systems
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