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.
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.
34174199
Selfish Stabilization
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.
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.
14224064
PeterNet: an emergent technology based radio access network architecture for next generation cellular wireless systems
For next generation wireless cellular networks, the radio access network (RAN) component is destined to evolve into a high-capacity, flexible and reconfigurable network architecture supporting smaller cell sites and newer technologies. Based on the well-known Petersen graph, in this paper we propose a RAN architecture, named PeterNet, that interconnects the network elements in a mesh topology. Focusing on optical wireless as the underlying transmission technology, we analyze our architecture on two key indices - carrier-class network reliability (99.999%) and infrastructure cost - providing comparative performance analysis with existing tree/star and regular grid networks. Furthermore, we generalize our architecture to what we call, the GPeterNet, which allows dynamic reconfiguration and redesign of the access network while leveraging the underlying salient features.
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
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.
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.
