32010004
Binary Self-Stabilization in Distributed Systems
Abstract Dijkstra introduced the problem of self-stabilization in distributed systems as an interesting exercise for achieving global convergence using local actions. In all the papers dealing with self-stabilizing systems so far, it has been assumed that each component machine of the distributed system has at least three states. This paper illustrates that it is feasible to design a self-stabilizing system with two-state or binary machines at the expense of a larger atomicity.
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.
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.
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.
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
25755124
An Algorithm for Computing a Convex and Simple Path of Bounded Curvature in a Simple Polygon

AbstractAbstract. In this paper we study the collision-free path planning problem for a point robot, whose path is of bounded curvature(i.e., constrained to have curvature at most 1), moving in the plane inside an n -sided simple polygon P . Given two points sand tinside Pand two directions of travel, one at sand one at t , the problem is to compute a convex and simple path of bounded curvature inside Pfrom sto tconsisting of straight-line segments and circular arcs such that (i) the radius of each circular arc is at least 1, (ii) each segment on the path is the tangent between the two consecutive circular arcs on the path, (iii) the given initial direction at sis tangent to the path at sand (iv) the given final direction at tis tangent to the path at t . We propose an O(n4)time algorithm for this problem. Using the notion of complete visibility, Pis pruned to another polygon P'such that any convex and simple path from sto tinside Palso remains inside P' . Then our algorithm constructs the locus of center of a circle of unit radius translating along the boundary of P'and, using this locus, the algorithm constructs a convex and simple path of bounded curvature. Our algorithm is based on the relationship between the Euclidean shortest path, link paths and paths of bounded curvature, and uses several properties derived here on convex and simple paths of bounded curvature. We also show that the path computed by our algorithm can be transformed in O(n)time to a minimalconvex and simple path of bounded curvature. Using this transformation and two necessary conditions proposed here for the shortest convex and simple path of bounded curvature, a minimalbounded curvature path is located in O(n4)time whose length, except in special situations involving arcs of length greater than π , is at most twice the length of a shortest convex and simple path of bounded curvature.

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.
14429447
iSimBioSys: a discrete event simulation platform for 'in silico' study of biological systems
With the availability of huge databases cataloguing the various molecular "parts" of complex biological systems, researchers from multiple disciplines have focused on developing modeling and simulation tools for studying the variability of cellular behavior at a system level - encompassing the dynamics arising from many species of interacting molecules. In this work, we present a system engineering approach to model biological processes. In this approach, a biological process is modeled as a collection of interacting functions driven in time by a set of discrete events. We focus on the discrete event simulation platform, called "iSimBioSys", which we have developed for studying the dynamics of cellular processes in silico. As a test-bed for studying our approach we model the two component PhoPQ system, responsible for the expression of several virulence genes in Salmonella Typhimurium. We analyzed the effect of extra cellular magnesium on the behavioral dynamics of this pathway using our framework and compared the results with an experimental system. We also analyze the performance of iSimBioSys, based on the model biological system, in terms of system usage and response.
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.