6238215
Fault-containing self-stabilizing algorithms
Self-stabilization provides a non-masking approach to fault tolerance. Given this fact, one would hope that in a self-stabilizing system, the amount of disruption caused by a fault is proportional to the severity of the fault. However, this is not true for many self-stabilizing systems. Our paper addresses this weakness of distributed self-stabilizing systems by introducing the notion of fault containment. Informally, a fault-containing self-stabilizing algorithm is one that contains the effects of limited transient faults while retaining the property of self-st abilization. The paper begins with a formal framework for specifying and evaluating fault-containing self-stabilizing protocols. Then, it is shown that self-stabilization and fault containment are goals that can conflict. For example, it is shown that imposing a O(1) bound on the worst case recovery time from a l-faulty state necessitates added overhead for stabilization: for some tasks, the O(1) recovery time implies sfiabilization time cannot be within O(1) rounds from the optimum value. The paper then presents a transformer T that maps any non-reactive self-stabilizing algorithm P into an equivalent fault-containing self-stabilizing algorithm Pf that can repair any l-faulty state in O(1) time with O(1) space overhead. This transformation is baaed on a novel stabilizing timer paradigm that significantly simplifies the ti=k of fault containment. The paper concludes by generalizing the transformer ‘T into a parameterized transformer 7(k) such that for varying k we obtain varying performance measures for Pf.
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.
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.
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.
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.
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.
972043
Stochastic Modeling of Cytoplasmic Reactions in Complex Biological Systems
The use of “in silico” stochastic event based modeling can identify the dynamic interactions of different processes in a complex biological system. This requires the computation of the time taken by different events in the system based on their biological functions. One such important event is the reactions between the molecules inside the cytoplasm of a cell. We present a mathematical formulation for the estimation of the reaction time between two molecules within a cell based on the system state. We derive expressions for the average and second moment of the time for reaction to be used by our stochastic event-based simulation. Unlike rate equations, the proposed model does not require the assumption of concentration stability for multiple molecule reactions.
5608135
Low-power weighted pseudo-random BIST using special scan cells
In this paper, a technique for weighted pseudo-random built-in self-test (BIST) of VLSI circuits is proposed, which uses special scan cells and a new weight selection algorithm to achieve low power dissipation. It is based on weighted pseudo-random scan testing in which only 3 weight values are used - 2 fixed values (0 or 1) and 1 random value (0.5). A new weight selection algorithm is used to select a set of weights that achieves high fault coverage while reducing power. The idea is to minimize power by careful selection of the set of scan cells having fixed values (0 or 1) in order to reduce switching activity. To implement this in hardware, a new scan cell design is proposed that can do scan and capture in the normal mode as well as fixed-bit mode. The new scan cell hardware increases the area of a typical circuit by less than 4%, but reduces power by as much as 96%, as indicated in experiments performed on benchmark circuits.
11538916
Reducing power consumption in memory ECC checkers
A method is proposed for reducing power consumption in memory ECC checker circuitry that provides SEC-DED. The degrees of freedom in selecting the parity check matrix are used to minimize power with little or no impact on area and delay. The power minimization method is applied to two popular SEC-DED codes: standard Hamming codes and odd-column-weight Hsiao codes. Experiments on actual memory traces of Spec and MediaBench benchmarks indicate that considering power in addition to area and delay when selecting the parity check matrix can result in power reductions of up to 27% for Hsiao codes and up to 41% for Hamming codes.
7750491
Revisiting correlations and scheduling in Web servers
Mathematical models play an important role in the design, analysis, control, optimization, management andplanning of Web server systems. To be most effective in each of these areas, such models must capture in sufficient detail the key characteristics of Web server workloads, the key characteristics of Web server scheduling policies for executing these workloads, and the impact of these workload and scheduling policy characteristics on Web server performance and related measures . Of particular interest in our study are very efficient mathematical methods that can be exploited online to support an increasingly important range of real-time applications (e .g., dynamic control of quality of service in Web servers to best satisfy service-level agreements), as well as in efficient interactive tools often used offline for many different purposes (e.g., what-ifanalysis and stochastic optimization for capacity planning). A significant body of research has investigated the workloads found in practice at a wide variety of Web server environments ; e.g ., see [1, 8, 18]. Most of these studies have demonstrated that the client request patterns exhibited at many different types of Web server environments have strong dependence structures and that the requested files sizes at these Web servers are independent and identically distributed (i .i .d.) according to a heavy-tailed or subexponential distribution . However, the vast majority of these studies appear to have completely ignored the issue of whether there is any correlation between the client request arrival times and the requested file sizes or the request service times. This includes studies of Web server workload characterization and generation, Web server performance models, and Web server scheduling policies . In this study, we consider data from various commercial Web server environments to revisit the issues of different forms of correlation in these Web server workloads and their implications on Web server performance and scheduling policies . Theresults ofour data analysis demonstrate the existence ofsignificant dependencies between the client request interarrival times and the corresponding file sizes and service times. Our analysis also shows a strong dependence structure within the interarrival process of client requests, whereas the sequence of service times is essentially i .i .d . To the best ofour knowledge, this is the first study to identify and quantify significant dependencies between the arrival and service processes in Web server environments (as opposed to network environments, where this issue goes all the way back to Kleinrock [15]). We then investigate the source of this cross correlation between the client request interarrival times and the corresponding file sizes and service times. The results of our data analysis support the view that such cross correlations are primarily due to certain mixing effects involving the superposition of different classes of client requests each with different service requirements . We next turn to consider a mathematical analysis of queueing Mark S. Squillante Mathematical Sciences Department IBM Thomas J. Watson Research Center Yorktown Heights, NY 10598, USA mss@watson .ibm .com