41043329
Fault-containing self-stabilization using priority scheduling
Schedulers play a vital role in the design of distributed algorithms. This paper introduces priority scheduling that can be used to design as well as reason about correctness proofs at a higher level of abstraction. The application of priority scheduling in solving problems related to stabilization and fault containment in spanning tree generation is presented. This paper also presents an implementation of the priority scheduling scheme.
17834776
Self-stabilizing algorithms for finding centers and medians of trees
Locating a center or a median in a graph is a fundamental graph-theoretic problem. Centers and medians are especially important in distributed systems because they are ideal locations for placing resources that need to be shared among dierent processes in a network. This paper presents simple self-stabilizing algorithms for locating centers and medians of trees. Since these algorithms are self-stabilizing, they can tolerate transient failures. In addition, they can automatically adjust to a dynamically changing tree topology. After the algorithms are presented, their correctness is proven and upper bounds on their time complexity are established. Finally, extensions of our algorithms to trees with arbitrary, positive edge costs are sketched.
3086074
An Exercise in Fault-Containment: Self-Stabilizing Leader Election
Self-stabilizing algorithms are designed to guarantee convergence to some desired stable state from arbitrary initial states arising out of an arbitrarily large number of faults. However, in a well-designed system, the simultaneous occurrence of a large number of faults is rare. It is therefore desirable to design algorithms that are not only self-stabilizing, but also have the ability to recover very fast from a bounded number of faults. As an illustration, we present a simple self-stabilizing leader election protocol that recovers in O(1) time from a state with a single transient fault on oriented rings. Only the faulty node and its two neighbors change their state during convergence to a stable state. Thus, the effect of a single fault is tightly contained around the fault. The technique for transforming a self-stabilizing algorithm into its fault-contained version is simple and general, and can be applied to other problems as well that satisfy certain properties.
43770248
Self-Stabilizing Algorithms for Finding Centers and Medians of Trees
Locating a center or a median in a graph is a fundamental graph-theoretic problem. Centers and medians are especially important in distributed systems because they are ideal locations for placing resources that need to be shared among different processes in a network. This paper presents simple self-stabilizing algorithms for locating centers and medians of trees. Since these algorithms are self-stabilizing, they can tolerate transient failures. In addition, they can automatically adjust to a dynamically changing tree topology. After the algorithms are presented, their correctness is proven and upper bounds on their time complexity are established. Finally, extensions of our algorithms to trees with arbitrary, positive edge costs are sketched.
9120365
A self-stabilizing algorithm for the maximum flow problem
Summary. The maximum flow problem is a fundamental problem in graph theory and combinatorial optimization with a variety of important applications. Known distributed algorithms for this problem do not tolerate faults or adjust to dynamic changes in network topology. This paper presents a distributed self-stabilizing algorithm for the maximum flow problem. Starting from an arbitrary state, the algorithm computes the maximum flow in an acyclic network in finitely many steps. Since the algorithm is self-stabilizing, it is inherently tolerant to transient faults. It can automatically adjust to topology changes and to changes in other parameters of the problem. The paper presents results obtained by extensively experimenting with the algorithm. Two main observations based on these results are (1) the algorithm requires fewer than n2 moves for almost all test cases and (2) the algorithm consistently performs at least as well as a distributed implementation of the well-known Goldberg-Tarjan algorithm for almost all test cases. The paper ends with the conjecture that the algorithm correctly computes a maximum flow even in networks that contain cycles.
11125013
A self-stabilizing algorithm for coloring planar graphs
SummaryThis paper describes an algorithm for coloring the nodes of a planar graph with no more than six colors using a self-stabilizing approach. The first part illustrates the coloring algorithm on a directed acyclic version of the given planar graph. The second part describes a selfstabilizing algorithm for generating the directed acyclic version of the planar graph, and combines the two algorithms into one.
1136530
A graph-theoretic approach for studying the convergence of fractal encoding algorithm
In this paper, we present a graph-theoretic interpretation of convergence of fractal encoding based on partial iterated function system (PIFS). First we have considered a special circumstance, where no spatial contraction has been allowed in the encoding process. The concept leads to the development of a linear time fast decoding algorithm from the compressed image. This concept is extended for the general scheme of fractal compression allowing spatial contraction (on averaging) from larger domains to smaller ranges. A linear time fast decoding algorithm is also proposed in this situation, which produces a decoded image very close to the result obtained by an ordinary iterative decompression algorithm.
616417
Synthesis of low power CED circuits based on parity codes
An automated design procedure is described for synthesizing circuits with low power concurrent error detection. It is based on pre-synthesis selection of a parity-check code followed by structure constrained logic optimization that produces a circuit in which all single point faults are guaranteed to be detected. Two new contributions over previous work include (1) the use of a k-way partitioning algorithm combined with local search to select a parity-check code, and (2) a methodology for minimizing power consumption in the CED circuitry. Results indicate significant reductions in area overhead due to the new code selection procedure as well as the ability to find low power implementations for use in power conscious applications.
1283500
GaMa: an evolutionary algorithmic approach for the design of mesh-based radio access networks
Wireless mesh based access networks are destined to play a pivotal role in next generation broadband systems. With the proliferation of mesh networks, a key issue for network designers is the design of an optimal mesh topology which minimizes cost while maintaining carrier-class features. In this paper, we formulate the design of an optimal mesh, taking network deployment cost, topological properties and carrier-grade reliability into account. Next, we present a genetic algorithm based algorithm (GaMa) for mesh topology design. We show that GaMa is capable of determining a generic mesh topology with carrier-class network features. The performance of the algorithm is compared with existing mesh topologies and gives improved results without the constraints of maintaining a regular topology
6735470
FraNtiC: A Fractal Geometric Framework for Mesh-Based Wireless Access Networks
The design of the access networks of next generation broadband wireless systems requires special attention in the light of changing network characteristics. In this paper, we present a mesh-based distributed radio access network (RAN) framework for future wireless systems. Using short, high bandwidth optical wireless links to interconnect the various network elements, we identify a generic fractal or self similar structure in the network. A mathematical model for the framework is presented and the benefits of its scale-invariant properties on robustness, reliability and flexibility analyzed. We focus on three design parameters - carrier-class network reliability, network exposure due to failure conditions and system cost. The dynamics of these parameters on our proposed architecture are studied and compared against existing access network topologies like tree/ring and square-grid. The generality and recursive nature of our framework lends itself to be applied in interconnecting various heterogeneous broadband wireless access networks of the future
748684
Detection probabilities of interconnect breaks: an analysis
An interconnect break is a break that occurs in the interconnect wiring, resulting in logic gate inputs being disconnected from the drivers and causing the wire to float. Interconnect breaks are the most common types of breaks in modern CMOS integrated circuits, so testing and detecting these breaks has become very important. This paper proposes a model by which standard tests for stuck-at-faults can be used to detect interconnect breaks in a circuit. This paper presents a worst-case analysis of the detection of these breaks and calculate the minimum number of test vectors required to detect breaks with a specified confidence level, using n-detection principles. To enhance the understanding of the breaks in the circuit, we present a statistical model based on the length distribution of the wires surrounding the floating wire where the break occurs. From the model we compute the detection probabilities of such breaks and show that the worst case of detection is when the bias voltage is the same as the logic threshold voltage.