A self-stabilizing algorithm for coloring planar graphs

Summary This 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. Sukumar Ghosh received his Ph.D. degree in Computer Science from Calcutta University in 1971. From 1969 to 1984, he taught at Jadavpur University, Calcutta. During 1976–77, he was a Fellow of the Alexander von Humboldt Foundation at the University of Dortmund, Germany. Since 1984, he is with the Department of Computer Science of the University of Iowa. His current research interests are in the areas of Distributed Systems, Petri Nets and Self-Stabilizating Systems. Mehmet Hakan Karaata received the Sc. B. degree in Computer Science and Engineering from Hacettepe University in Turkey in 1987, and the M.S. degree in Computer Science from the University of Iowa in 1990. He is currently studying towards his Ph.D. at the same university. His research interests are in the areas of Distributed Systems, Self-Stabilizing Systems and Database Systems.This research was supported in part by the National Science Foundation under grant CCR-9109078, and the Old Gold Summer Fellowship of the University of Iowa. An abstract of this paper was presented at the 29th Allerton Conference on Control, Communication & Computing in October 1991.     

A 4n-move self-stabilizing algorithm for the minimal dominating set problem using an unfair distributed daemon

A distributed system is self-stabilizing if, regardless of its initial state, the system is guaranteed to reach a legitimate (i.e., correct) state in finite time. In 2007, Turau proposed the first linear-time self-stabilizing algorithm for the minimal dominating set (MDS) problem under an unfair distributed daemon [9]; this algorithm stabilizes in at most 9n moves, where n is the number of nodes in the system. In 2008, Goddard et al. [4] proposed a 5n-move algorithm. In this paper, we present a 4n-move algorithm.     

An efficient distributed algorithm for maximum matching in general graphs

We present a distributed algorithm for maximum cardinality matching in general graphs. On a general graph withn vertices, our algorithm requiresO(n ^5/2) messages in the worst case. On trees, our algorithm computes a maximum matching usingO(n) messages after the election of a leader.Work on this paper has been supported by the Office of Naval Research under Contract N00014-85-K-0570.     

Observations on non-silent self-stabilizing algorithms in sensor networks with probabilistically intermittent link failures

A wireless sensor network is a set of nodes, each is equipped with a sensing device and a wireless communication device. Because centralized control is hard to achieve in a large scale sensor network, self-∗ is a key concept in the design of a wireless sensor network. Self-stabilization is one of the self-∗ properties, and it is one of the most promising theoretical backgrounds for self-organizing wireless sensor network protocols. Herman [T. Herman, Models of self-stabilization and sensor networks, in: Proceedings of the 5th International Workshop of Distributed Computing, IWDC, 2003, pp. 205-214] proposed Cached Sensornet Transform (CST for short) for design and implementation of self-stabilizing algorithms for sensor networks. It transforms a self-stabilizing algorithm in a high-level computational model to a program for sensor networks. Our contribution in this paper is threefold. We show that there exists a non-silent algorithm that behaves correctly in a high-level computational model but its transformed version by CST does not behave correctly if packets are lost. We show a sufficient condition for original algorithms and networks such that the algorithm transformed by CST behaves correctly. As a case study, we present a token circulation algorithm that behaves correctly by CST and derive the upper bound of its expected convergence time.     

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.     

Fully dynamic algorithms for permutation graph coloring

We introduce a dynamic model for maintaining permutation graph coloring. Our motivation comes from the strait type river routing problem in VLSI. This paper presents fully dynamic algorithms for the permutation graph coloring problem. These algorithms are designed to handle Insert and Delete operations and answer some queries. The aim is to provide for running times that are asymptotically more efficient than recomputation (off-line algorithms that run in 0(n logw) time, are known [5,6,10,3]). First, the algorithm A^ that runs in 0(n) uniform running time per Insert/Delete operation is presented. Second, a more sophisticated data structure leads to the algorithm A2 that runs in (9(m logw) uniform running time per Insert I Delete, where m denotes the number of chains in the decomposition. It follows from [7,4] that the running time of A2 when the points from the dynamically changing set are drawn independently from a uniform distribution on the unit square is G(yfn logn) per Insert/Delete in probability. Third, we sketch a composite algorithm A3 that switches between A± and A2 guarantees an amortized running time of (min{n,m logw)) per Insert/Delete. Finally, we outline a number of applications     

Polynomial-time algorithms for weighted efficient domination problems in AT-free graphs and dually chordal graphs

An efficient dominating set (or perfect code) in a graph is a set of vertices the closed neighborhoods of which partition the vertex set of the graph. The minimum weight efficient domination problem is the problem of finding an efficient dominating set of minimum weight in a given vertex-weighted graph; the maximum weight efficient domination problem is defined similarly. We develop a framework for solving the weighted efficient domination problems based on a reduction to the maximum weight independent set problem in the square of the input graph. Using this approach, we improve on several previous results from the literature by deriving polynomial-time algorithms for the weighted efficient domination problems in the classes of dually chordal and AT-free graphs. In particular, this answers a question by Lu and Tang regarding the complexity of the minimum weight efficient domination problem in strongly chordal graphs.     

Linear self-stabilizing algorithms for the independent and dominating set problems using an unfair distributed scheduler

This paper presents distributed self-stabilizing algorithms for the maximal independent and the minimal dominating set problems. Using an unfair distributed scheduler the algorithms stabilizes in at most max{3n−5,2n} resp. 9n moves. All previously known algorithms required O(n²) moves.     

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 n ² 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. Received: October 1995 / Accepted: February 1997     

A note on 2-facial coloring of plane graphs

An l-facial coloring of a plane graph is a vertex coloring such that any two different vertices joined by a facial walk of length at most l receive distinct colors. It is known that every plane graph admits a 2-facial coloring using 8 colors [D. Král, T. Madaras, R. Škrekovski, Cyclic, diagonal and facial coloring, European J. Combin. 3-4 (26) (2005) 473-490]. We improve this bound for plane graphs with large girth and prove that if G is a plane graph with girth g?14 (resp. 10, 8) then G admits a 2-facial coloring using 5 colors (resp. 6, 7). Moreover, we give exact bounds for outerplanar graphs and K₄-minor free graphs.     

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     

On-line string matching algorithms: survey and experimental results

In this paper we present a short survey and experimental results for well known sequential string matching algorithms. We consider algorithms based on different approaches including classical, suffix automata, bit-parallelism and hashing. We put special emphasis on algorithms recently presented such as Shift-Or and BNDM algorithms. We compare these algorithms in terms of the number of character comparisons and the running time for four different types of text: binary alphabet, alphabet of size 8, English alphabet and DNA alphabet.     

The general maximum matching algorithm of micali and vazirani

We give a clear exposition of the algorithm of Micali and Vazirani for computing a maximum matching in a general graph. This is the most efficient algorithm known for general matching. On a graph withn vertices andm edges this algorithm runs inO(n ^1/2 m) time.Work on this paper has been supported by the Office of Naval Research under Contract N00014-85-K-0570 and by the Eastman Kodak Company.     

随机图的均匀边染色算法

图的均匀边染色是指图中任意两条相邻的边都分配到不同的颜色,且任意两个色类的颜色个数最大相差1。对图 进行均匀边染色所需的最少颜色数叫做 的均匀边色数。本文提出了一种启发式算法,能够求解图的最小均匀边色数。该算法根据均匀边染色条件,设计了两个子目标函数和一个总目标函数,借助染色矩阵的色补矩阵迭代交换,逐步寻优,直到找到最优解时结束。本文给出了详细的算法设计流程,并且进行了大量的测试和分析,实验结果表明,该算法可以高效地求出给定点数的图的最小均匀边色数,算法时间复杂度不超过 。