Self-stabilizing defeat status computation: dealing with conflict management in multi-agent systems

The role of argumentation in supporting various forms of interaction among possibly conflicting autonomous agents has been explicitly recognized in the literature. In argumentation, conflict management is carried out by the formal process of defeat status computation. In this paper we consider the generalization of this process to a distributed setting. We show that significant stabilization problems may arise even in relatively simple cases. A fundamental negative result is then proved: no general self-stabilizing algorithm exists for distributed defeat status computation, indicating that self-stabilizing algorithms for this problem can be defined only under specific conditions. Accordingly, we focus on two cases: an algorithm tailored to a specific family of inference graphs, that include only rebutting defeaters, and an algorithm that applies to any inference graph, also including undercutting defeaters, but may provide (cautiously) incorrect results for some nodes. For both algorithms the worst-case round complexity is analyzed and it is proved that no algorithms with lower complexity exist for the same tasks.     

Self-stabilizing group communication in directed networks

This paper presents the first self-stabilizing group membership service, multicast service, and resource allocation service for directed networks. The first group communication algorithm is based on a token circulation over a virtual ring. The second algorithm is based on construction of distributed spanning trees. In addition, a technique is presented that emulates, in a self-stabilizing fashion, any undirected communication network over strongly connected directed networks, is presented. A resource allocation asynchronous algorithm for strongly connected directed networks is presented.Received: 23 July 2003, Published online: 29 June 2004Partially supported by NSF Award CCR-0098305, IBM faculty award, STRIMM consortium, and Israel ministry of defense.     

Self-stabilizing smoothing and balancing networks

A smoothing network is a distributed data structure that accepts tokens on input wires and routes them to output wires. It ensures that however imbalanced the traffic on input wires, the numbers of tokens emitted on output wires are approximately balanced. Prior work on smoothing networks always assumed that such networks were properly initialized. In a real distributed system, however, network switches may be rebooted or replaced dynamically, and it may not be practical to determine the correct initial state for the new switch. Prior analyses do not work under these new assumptions. This paper makes the following contributions. First, we show that some well-known 1-smoothing networks, known as counting networks, when started in an arbitrary initial state (perhaps chosen by an adversary), remain remarkably smooth, degrading from 1-smooth to (log n)-smooth, where n is the number of input/output wires. For the networks that we consider, we show that the above (log n) bound for the smoothness is tight. Our second contribution is to show how any balancing network can be made self-stabilizing with the addition of local stabilization actions and state, which restore the network back to a “legal state” even if it starts out in an illegal state. A preliminary version of this work appeared in the Proceedings of The 23rd International Conference on Distributed Computing Systems, Providence, Rhode Island, USA.     

Self-stabilizing byzantine asynchronous unison

We explore asynchronous unison in the presence of systemic transient and permanent Byzantine faults in shared memory. We observe that the problem is not solvable under a less than strongly fair scheduler or for system topologies with maximum node degree greater than two.     

Self-stabilizing algorithm for checkpointing in a distributed system

If the variables used for a checkpointing algorithm have data faults, the existing checkpointing and recovery algorithms may fail. In this paper, self-stabilizing data fault detecting and correcting, checkpointing, and recovery algorithms are proposed in a ring topology. The proposed data fault detection and correction algorithms can handle data faults; at most one per process, but in any number of processes. The proposed checkpointing algorithm can deal with concurrent multiple initiations of checkpointing and data faults. A process can recover from a fault, using the proposed recovery algorithm in spite of multiple data faults present in the system. All the proposed algorithms converge in O(n)$O(n)$ steps, where n$n$ is the number of processes. The algorithm can be extended to work for general topologies too.     

Self-stabilizing depth-first token circulation on networks

Summary This paper proposes a self-stabilizing protocol which circulates a token on a connected network in nondeterministic depth-first-search order, rooted at a special node. Starting with any initial state in which the network may have no token at all or more than one token, the protocol eventually makes the system stabilize in states having exactly one circulating token. With a slight modification to the protocol —by removing nondeterminism in the search — a depth-first-search tree on the network can be constructed. The proposed protocol runs on systems that allow parallel operations. Shing-Tsaan Huang was born in Taiwan on September 4, 1949. He got his Ph.D. degree in 1985 from Department of Computer Science, University of Maryland at College Park. Before he pursued his Ph.D. degree, he had worked several years in the computer industry in Taiwan. Professor Huang is currently the chairman of the Department of Computer Science, Tsing Hua University, Taiwan, Republic of China. His research interests include interconnection networks, operating systems and distributed computing. He is a senior member of the IEEE Computer Society and a member of the Association for Computing Machinery. Nian-Shing Chen was born in Taiwan on October 21, 1961. He received his Ph.D. degree in computer science from National Tsing Hua University in 1990. Dr. Chen is currently an associate professor with the Department of Information Management at Sun Yat-Sen University of Taiwan. His research interests include distributed systems, computer networks, computer viruses and expert systems. He is a member of IEEE and Phi Tau Phi honorary society.This research is supported by National Science Council of the Republic of China under the contract NSC81-0408-E-007-05 and NSC82-0408-E-007-027     

Self-stabilizing multi-token rings

Summary A distributed system consists of a set of loosely connected machines that do not share a global memory. The system isself-stabilizing if it can be started in any global state and achieves consistency all by itself. This also means that the system can deal withinfrequent errors. This paper presents self-stabilizing multi-token rings. A multitoken ring is a generalization of a (one-)token ring. The algorithms presented are generalizations of a self-stabilizing mutual exclusion algorithm by Dijkstra [5] which can also be viewed as a token ring. We develop the algorithms in a stepwise manner, to show how and why we arrived at the final multi-token rings. The final parameterized algorithm represents a set of algorithms, one for each choice of the parameter. This enables one to select the algorithm with an optimal trade-off in desired flexibility versus memory requirements and stabilization time. Mitchell Flatebo received the B.S. degree in Mathematics (1990), the B.S. degree in Computer Science (1990), the M.S. degree in Mathematics (1992), and the M.S. degree in Computer Science (1993) from the University of Nevada, Las Vegas. He is currently a software engineer for Loral Space and Range Systems. His research interests include distributed systems, fault-tolerant computing, and self-stabilization. Ajoy Kumar Datta received the Ph.D. degree in Computer Science from the Jadavpur University, Calcutta, India in 1983. He is currently an Associate Professor of Computer Science at the University of Nevada, Las Vegas. His area of research is distributed and fault-tolerant computing —algorithms and self-stabilization. Anneke Schoone received an M.Sc. degree in Biology in 1978, an M.Sc. degree in Mathematics in 1981, and a Ph.D. degree in Computer Science in 1991 from Utrecht University (The Netherlands). Currently she is a senior research associate at the Department of Computer Science of Utrecht University, supported by ESPRIT Basic Research Action No. 7141 (project ALCOM II:Algorithms and Complexity) of the EC. Her research interests include assertional verification of distributed algorithms and the concept of self-stabilization.The research of this author was supported partially by the ESPRIT Basic Research Action No. 7141 (project ALCOM II:Algorithms and Complexity), and partially by the Netherlands Organization for Scientific Research (NWO) under contract NF 62-376 (NFI project ALADDIN:Algorithmic Aspects of Parallel and Distributed Systems)     

Self-stabilizing minimum degree spanning tree within one from the optimal degree

We propose a self-stabilizing algorithm for constructing a Minimum Degree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most Δ^∗+1, where Δ^∗ is the minimum possible maximum degree of a spanning tree of the network.To the best of our knowledge, our algorithm is the first self-stabilizing solution for the construction of a minimum degree spanning tree in undirected graphs. The algorithm uses only local communications (nodes interact only with the neighbors at one hop distance). Moreover, the algorithm is designed to work in any asynchronous message passing network with reliable FIFO channels. Additionally, we use a fine grained atomicity model (i.e., the send/receive atomicity). The time complexity of our solution is O(mn²logn) where m is the number of edges and n is the number of nodes. The memory complexity is O(δlogn) in the send-receive atomicity model (δ is the maximal degree of the network).     

Self-stabilizing token circulation in uniform networks

Summary.  A self-stabilizing protocol for token circulation in a connected, uniform network of nodes with prime size is proposed. A network of nodes is said to be uniform if all nodes are logically equivalent and identically programmed. The protocol has the ability to handle any arbitrary initial state in which more than one token or no token at all exist in the network and makes the network eventually have one and only one token fairly circulating among the nodes of the network. The protocol is deterministic, its self-stabilization property is proven under the assumption of a serial and fair scheduler. Received: July 1995 / Accepted: February 1997     

Self-stabilizing leader election in optimal space under an arbitrary scheduler

A silent self-stabilizing asynchronous distributed algorithm, SSLE, is given for the leader election problem in a connected unoriented (bidirectional) network with unique IDs. SSLE also constructs a BFS tree on the network rooted at that leader. SSLE uses O(logn) space per process and stabilizes in O(n) rounds, against the unfair daemon, where n is the number of processes in the network.     

Self-stabilizing 2^m-clock for unidirectional rings of odd size

Summary. In this paper, we propose a self-stabilizing K-clock protocol for unidirectional rings with odd size, where and m is any positive integer. Besides the variable for maintaining the clock, the proposed protocol only requires one additional bit. The worst-case stabilizing time is ), where n is the ring size. Received: July 1998 / Accepted: January 1999     

HyperTree for self-stabilizing peer-to-peer systems

Peer-to-peer systems are prone to faults; Therefore, it is extremely important to design peer-to-peer systems that automatically regain consistency or, in other words, are self-stabilizing. In order to achieve the above, we present a deterministic structure that defines the entire (IP) pointers structure among the machines, for every n machines; i.e., defines the next hop for the insert, delete, and search procedures of the peer-to-peer system. Thus, the consistency of the system is easily defined, monitored, verified, and repaired. We present the HyperTree (distributed) structure, which supports the peer-to-peer procedures while ensuring that the out-degree and the in-degree (the number of outgoing/ incoming pointers) are b log _b n where n is the actual number of machines and b is an integer parameter greater than 1. Moreover, the HyperTree ensures that the maximal number of hops involved in each procedure is bounded by log _b n. A self-stabilizing peer-to- peer distributed algorithm based on the HyperTree is presented. This work was partially supported by IBM Faculty Award, NSF Grant 0098305, the Israeli Ministry of Trade and Industry, the Rita Altura Trust Chair in Computer Sciences and the Lynne and William Frankel Center for Computer Sciences. The work was done while Ronen I. Kat was a PhD student at Ben-Gurion University of the Negev. An preliminary version was published in the proceedings of the third IEEE International Symposium on Network Computing and Applications (NCA’04).     

Self-stabilizing algorithm for high service availability in spite of concurrent topology changes in ad hoc mobile networks

Mobile nodes in ad hoc networks move freely and run out of battery power so quickly, which leads to frequent network partitioning. Network partitioning considerably reduces service availability when the server node is not in the same partition as the client nodes. In order to provide a continuous service availability for all mobile nodes, we propose a self-stabilizing algorithm that can tolerate multiple concurrent topological changes and can incur a cost of one server per long-lived connected component. By using (1) the time interval-based computations concept that distinguishes between disjoint and concurrent computations, and (2) Markov chain model, the proposed algorithm can within a finite time converge to a legitimate state even if topological changes occur during the convergence time. Our simulation results show that the algorithm can ensure very high service availability, and each node has a strong path to the server of its network component over 98% of the time.     

Self-stabilizing depth-first token circulation in arbitrary rooted networks

Abstract. We present a deterministic distributed depth-first token passing protocol on a rooted network. This protocol uses neither the processor identifiers nor the size of the network, but assumes the existence of a distinguished processor, called the root of the network. The protocol is self-stabilizing, meaning that starting from an arbitrary state (in response to an arbitrary perturbation modifying the memory state), it is guaranteed to reach a state with no more than one token in the network. Our protocol implements a strictly fair token circulation scheme. The proposed protocol has extremely small state requirement – only states per processor, i.e., bits per processor, where is the degree of the network. The protocol can be used to implement a strictly fair distributed mutual exclusion in any rooted network. This protocol can also be used to construct a DFS spanning tree. Received: July 1998 / Accepted: April 2000     

Self-stabilizing real-time OPS5 production systems

We examine the task of constructing bounded-time self-stabilizing rule-based systems that take their input from an external environment. Bounded response-time and self-stabilization are essential for rule-based programs that must be highly fault-tolerant and perform in a real-time environment. We present an approach for solving this problem using the OPS5 programming language as it is one of the most expressive and widely used rule-based programming languages. Bounded response-time of the program is ensured by constructing the state space graph so that the programmer can visualize the control flow of the program execution. Potential infinite firing sequences, if any, should be detected and the involved rules should be revised to ensure bounded termination. Both the input variables and internal variables are made fault-tolerant from corruption caused by transient faults via the introduction of new self-stabilizing rules in the program. Finally, the timing analysis of the self-stabilizing OPS5 program is shown in terms of the number of rule firings and the comparisons performed in the Rete network.     

Unifying stabilization and termination in message-passing systems

The paper dispels the myth that it is impossible for a message-passing program to be both terminating and stabilizing. We consider a rather general notion of termination: a terminating program eventually stops its execution after the environment ceases to provide input. We identify termination-symmetry to be a necessary condition for a problem to admit a solution with such properties. Our results do confirm that a number of well-known problems (e.g., consensus, leader election) do not allow a terminating and stabilizing solution. On the flip side, they show that other problems such as mutual exclusion and reliable-transmission allow such solutions. We present a message-passing solution to the mutual exclusion problem that is both stabilizing and terminating. We also describe an approach of adding termination to a stabilizing program. To illustrate this approach, we add termination to a stabilizing solution for the reliable transmission problem.Published online: 15 November 2004Anish Arora: Supported in part by DARPA contract OSU-RF #F33615-01-C-1901,NSF grant NSF-CCR-9972368, Ohio State University Fellowship,and 2002-2003,2003-2004 grants from Microsoft Research.Mikhail Nesterenko: Supported in part by DARPA contract OSU-RF #F33615-01-C-1901 and byNSF CAREER Award 0347485Some of the results in this paper were presented at the 21st International Conference on Distributed Computing Systems, Mesa, Arizona, April 2001, pp 99-106. Correspondence to: Mikhail Nesterenko     

Snap-stabilization in message-passing systems

In this paper, we tackle the problem of snap-stabilization in message-passing systems. Snap-stabilization allows designing protocols that withstand transient faults: indeed, any computation that is started after faults cease immediately satisfies the expected specification.     

Distributed computing on cluster systems

Message Passing Interface (MPI) allows a group of computers in a network to be specified as a cluster system. It provides the routines for task activation and communication. Writing programs for a cluster system is a difficult job. In this paper the Message-passing Interface is presented. Parallel programs using the WMPI, a version of MPI, to solve the pi(π) calculation the quick sort algorithm and the Torsion problem are presented. The programs are written and compiled in Microsoft Visual C+ +.