An efficient fault-containing self-stabilizing algorithm for the shortest path problem

Shortest path finding has a variety of applications in transportation and communication. In this paper, we propose a fault-containing self-stabilizing algorithm for the shortest path problem in a distributed system. The improvement made by the proposed algorithm in stabilization times for single-fault situations can demonstrate the desirability of an efficient fault-containing self-stabilizing algorithm. For single-fault situations, the worst-case stabilization time of the proposed algorithm is O(Δ), where Δ is the maximum node degree in the system, and the contamination number of the proposed algorithm is 1.     

An energy-efficient,self-stabilizing and distributed algorithm for maximal independent set construction in wireless sensor networks

Maximal independent set (MIS) is a very important structure that provides data aggregation, topology control and routing for wireless sensor networks (WSNs). Energy-efficient and fault-tolerant construction of MIS on WSNs is one of the vital tasks. A distributed sensor network is self-stabilizing if it can initially start at any state and regain a legal state in a finite time without any external intervention. Self-stabilization is a considerable method to provide fault tolerance in WSNs. This paper presents a distributed self-stabilizing MIS algorithm which is an improved version of Turau’s algorithm under a fully distributed scheduler for WSNs. The proposed algorithm is theoretically analyzed and evaluated with its counterparts. The proposed algorithm is compared with the other studies through testbed experiments on IRIS nodes and simulations on TOSSIM environment. It is shown that the proposed algorithm outperforms other algorithms in terms of move count and energy consumption.     

An anonymous self-stabilizing algorithm for 1-maximal independent set in trees

We present an anonymous, constant-space, self-stabilizing algorithm for finding a 1-maximal independent set in tree graphs (and some rings). We show that the algorithm converges in O(n²) moves under any central daemon (one that at each time-step selects one of the privileged nodes to move).     

A self-stabilizing algorithm for bridge finding

Summary. A self-stabilizing algorithm is presented in this paper that finds the bridges of a connected undirected graph on a distributed or network model of computation after moves. The algorithm is resilient to transient faults and does not require initialization. In addition, a correctness proof of the algorithm is provided. The paper concludes with remarks on the time complexity of the algorithm. Received: July 1997 / Accepted: January 1999     

An efficient parallel algorithm for computing a large independent set in a planar graph

Let (G) denote the independence number of a graphG, that is the maximum number of pairwise independent vertices inG. We present a parallel algorithm that computes in a planar graphG = (V, E), an independent set such that ¦I¦ (G)/2. The algorithm runs in timeOlog² n) and requires a linear number of processors. This is achieved by denning a new set of reductions that can be executed locally and simultaneously; furthermore, it is shown that a constant fraction of the vertices in the graph are reducible. This is the best known approximation scheme when the number of processors available is linear; parallel implementation of known sequential algorithms requires many more processors.Joseph Naor was supported by Contract ONR N00014-88-K-0166. Most of this work was done while he was a post-doctoral fellow at the Department of Computer Science, University of Southern California, Los Angeles, CA 90089-0782, USA.     

An efficient parallel algorithm for computing a large independent set in a planar graph

Let α(G) denote the independence number of a graphG, that is the maximum number of pairwise independent vertices inG. We present a parallel algorithm that computes in a planar graphG = (V, E), an independent set \(I \subseteq V\) such that ¦I¦≥ α (G)/2. The algorithm runs in timeOlog² n) and requires a linear number of processors. This is achieved by denning a new set of reductions that can be executed “locally” and simultaneously; furthermore, it is shown that a constant fraction of the vertices in the graph are reducible. This is the best known approximation scheme when the number of processors available is linear; parallel implementation of known sequential algorithms requires many more processors.     

A new self-stabilizing maximal matching algorithm

The maximal matching problem has received considerable attention in the self-stabilizing community. Previous work has given several self-stabilizing algorithms that solve the problem for both the adversarial and the fair distributed daemon, the sequential adversarial daemon, as well as the synchronous daemon. In the following we present a single self-stabilizing algorithm for this problem that unites all of these algorithms in that it has the same time complexity as the previous best algorithms for the sequential adversarial, the distributed fair, and the synchronous daemon. In addition, the algorithm improves the previous best time complexities for the distributed adversarial daemon from O(n²)$O\left(n^2\right)$ and O(δm)$O\left(\delta m\right)$ to O(m)$O\left(m\right)$ where n$n$ is the number of processes, m$m$ is the number of edges, and δ$\delta$ is the maximum degree in the graph.     

Beeping a maximal independent set

We consider the problem of computing a maximal independent set (MIS) in an extremely harsh broadcast model that relies only on carrier sensing. The model consists of an anonymous broadcast network in which nodes have no knowledge about the topology of the network or even an upper bound on its size. Furthermore, it is assumed that an adversary chooses at which time slot each node wakes up. At each time slot a node can either beep, that is, emit a signal, or be silent. At a particular time slot, beeping nodes receive no feedback, while silent nodes can only differentiate between none of its neighbors beeping, or at least one of its neighbors beeping. We start by proving a lower bound that shows that in this model, it is not possible to locally converge to an MIS in sub-polynomial time. We then study four different relaxations of the model which allow us to circumvent the lower bound and find an MIS in polylogarithmic time. First, we show that if a polynomial upper bound on the network size is known, it is possible to find an MIS in $\mathcal O (\log ^3 n)$ time. Second, if we assume sleeping nodes are awoken by neighboring beeps, then we can also find an MIS in $\mathcal O (\log ^3 n)$ time. Third, if in addition to this wakeup assumption we allow sender-side collision detection, that is, beeping nodes can distinguish whether at least one neighboring node is beeping concurrently or not, we can find an MIS in $\mathcal O (\log ^2 n)$ time. Finally, if instead we endow nodes with synchronous clocks, it is also possible to find an MIS in $\mathcal O (\log ^2 n)$ time.     

An efficient algorithm for finding ideal schedules

We study the problem of scheduling unit execution time jobs with release dates and precedence constraints on two identical processors. We say that a schedule is ideal if it minimizes both maximum and total completion time simultaneously. We give an instance of the problem where the min-max completion time is exceeded in every preemptive schedule that minimizes total completion time for that instance, even if the precedence constraints form an intree. This proves that ideal schedules do not exist in general when preemptions are allowed. On the other hand, we prove that, when preemptions are not allowed, then ideal schedules do exist for general precedence constraints, and we provide an algorithm for finding ideal schedules in O(n ³) time, where n is the number of jobs. In finding such ideal schedules we resolve a conjecture of Baptiste and Timkovsky (Math. Methods Oper. Res. 60(1):145–153, 2004) Further, our algorithm for finding min-max completion-time schedules requires only O(n ³) time, while the most efficient solution to date has required O(n ⁹) time.     

一个新的极大独立集算法及独立数的界

最大独立集问题是图论中典型的组合优化问题,有着广泛的实际应用价值。分析了现有独立数的界公式后给出了新的上界公式,并通过分析贪婪算法和独立集自身的特征,给出了新的求解极大独立集的算法,并证明了其确定性。然后用实例验证了该算法的有效性。     

An efficient algorithm for finding a collision-free path among polyhedral obstacles

The use of graph search algorithms on a so called “visibility graph” is a common approach to finding a minimum-distance collision-free path among polyhedral obstacles in a 2D environment. Complexity of the search can be greatly reduced by reducing the size of the graph. The focus of this article is to provide an algorithm aimed at constructing a subvisibility graph using only “necessary” obstacles, i.e., excluding as many obstacles as possible whose vertices are never via points of the shortest collision-free path.     

一种高效的最大频繁项挖掘算法

提出一种下三角矩阵的最大频繁项挖掘算法DTMFIM,首先将事务数据库映射到一个布尔矩阵中,并产生频繁1-项集,然后根据频繁1-项集生产频繁2-项集,且对其结果用下三角的布尔矩阵存储,最大频繁项集可通过这个下三解矩阵求得,在求解过程中不断地压缩这个下三角矩阵.实验表明,此算法实现简洁、高效,与经典的Apriori算法及部分Apfiori改进算法相比,特别对大事务集、长项目集数据挖掘效果更为明显.     

An efficient algorithm for finding the CSG representation of a simple polygon

Modeling two-dimensional and three-dimensional objects is an important theme in computer graphics. Two main types of models are used in both cases: boundary representations, which represent the surface of an object explicitly but represent its interior only implicitly, and constructive solid geometry representations, which model a complex object, surface and interior together, as a boolean combination of simpler objects. Because neither representation is good for all applications, conversion between the two is often necessary.We consider the problem of converting boundary representations of polyhedral objects into constructive solid geometry (CSG) representations. The CSG representations for a polyhedronP are based on the half-spaces supporting the faces ofP. For certain kinds of polyhedra this problem is equivalent to the corresponding problem for simple polygons in the plane. We give a new proof that the interior of each simple polygon can be represented by a monotone boolean formula based on the half-planes supporting the sides of the polygon and using each such half-plane only once. Our main contribution is an efficient and practicalO(n logn) algorithm for doing this boundary-to-CSG conversion for a simple polygon ofn sides. We also prove that such nice formulae do not always exist for general polyhedra in three dimensions.The first author would like to acknowledge the support of the National Science Foundation under Grants CCR87-00917 and CCR90-02352. The fourth author was supported in part by a National Science Foundation Graduate Fellowship. This work was begun while the first author was visiting the DEC Systems Research Center.     

A self-stabilizing algorithm to maximal 2-packing with improved complexity

In self-stabilization, each node has a local view of the distributed network system, in a finite amount of time the system converges to a global setup with desired property, in this case establishing a 2-packing set. Using a graph G=(V,E)$G=(V,E)$ to represent the network, a subset S⊆V$S\subseteq V$ is a 2-packing if ∀i∈V:|N[i]∩S|?1$\forall i\in V:|N[i]\cap S|?1$. In this paper, we first propose an ID-based, constant space, self-stabilizing algorithm that stabilizes to a maximal 2-packing in an arbitrary graph. We show that the algorithm stabilizes in O(mn)$O(mn)$ moves under any scheduler (such as a distributed daemon). Secondly, we show that the algorithm stabilizes in O(n²)$O(n^2)$ rounds under a synchronous daemon where every privileged node moves at each round.     

An efficient approximation algorithm for finding a maximum clique using Hopfield network learning

In this article, we present a solution to the maximum clique problem using a gradient-ascent learning algorithm of the Hopfield neural network. This method provides a near-optimum parallel algorithm for finding a maximum clique. To do this, we use the Hopfield neural network to generate a near-maximum clique and then modify weights in a gradient-ascent direction to allow the network to escape from the state of near-maximum clique to maximum clique or better. The proposed parallel algorithm is tested on two types of random graphs and some benchmark graphs from the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS). The simulation results show that the proposed learning algorithm can find good solutions in reasonable computation time.