Skip Graph is a promising distributed data structure for large scale systems and known for its capability of range queries. Although several methods of routing range queries in Skip Graph have been proposed, they have inefficiencies such as a long path length or a large number of messages. In this paper, we propose a novel routing method for range queries named Split-Forward Broadcasting (SFB). SFB introduces a divide-and-conquer approach, enabling nodes to make full use of their routing tables to forward a range query. It brings about a shorter average path length than existing methods, as well as a smaller number of messages by avoiding duplicate transmission. We clarify the characteristics and effectiveness of SFB through both analytical and experimental comparisons. The results show that SFB can reduce the average path length roughly 30% or more compared with a state-of-the-art method.

A radio network (RN for short) is a distributed system with no central arbiter, consisting of n radio transceivers, henceforth referred to as stations. We assume that the stations run on batteries and expends power while broadcasting/receiving a data packet. Thus, the most important measure to evaluate protocols on the radio network is the number of awake time slots, in which a station is broadcasting/receiving a data packet. We also assume that the stations are identical and have no unique ID number, and no station knows the number n of the stations. For given n keys one for each station, the ranking problem asks each station to determine the number of keys in the RN smaller than its own key. The main contribution of this paper is to present an optimal randomized ranking protocol on the k-channel RN. Our protocol solves the ranking problem, with high probability, in O(+log n) time slots with every station being awake for at most O(log n) time slots. We also prove that any randomized ranking protocol is required to run in expected Ω(+log n) time slots with at least one station being awake for expected Ω(log n) time slots. Therefore, our ranking protocol is optimal.

In this work we present an energy efficient leader election protocol for anonymous radio network populated with n mobile stations. Previously, Nakano and Olariu have presented a leader election protocol that terminates, with probability exceeding 1- (f ≥ 1), in log log n+o(log log n)+O(log f) time slots [14]. As the above protocol works under the assumption that every station has the ability to transmit and monitor the channel at the same time, it requires every station to be equipped with two transceivers. This assumption, however, is unrealistic for most mobile stations due to constraints in cost, size, and energy dissipation. Our main contribution is to show that it is possible to elect a leader in an anonymous radio network where each station is equipped with a single transceiver. Quite surprisingly, although every station has only one transceiver, our leader election protocol still runs, with probability exceeding 1- (f ≥ 1), in log log n+o(log log n)+O(log f) time slots. Moreover, our leader election protocol needs only expected O(n) total awake time slots, while Nakano and Olariu's protocol needs expected O(nlog log n) total awake time slots. Since every leader election protocol needs at least Ω(n) awake time slots, our leader election protocol is optimal in terms of the expected awake time slots.

We consider the problem of computing the optimal swap edges of a shortest-path tree. This problem arises in designing systems that offer point-of-failure shortest-path rerouting service in presence of a single link failure: if the shortest path is not affected by the failed link, then the message will be delivered through that path; otherwise, the system will guarantee that, when the message reaches the node where the failure has occurred, the message will then be re-routed through the shortest detour to its destination. There exist highly efficient serial solutions for the problem, but unfortunately because of the structures they use, there is no known (nor foreseeable) efficient distributed implementation for them. A distributed protocol exists only for finding swap edges, not necessarily optimal ones. We present two simple and efficient distributed algorithms for computing the optimal swap edges of a shortest-path tree. One algorithm uses messages containing a constant amount of information, while the other is tailored for systems that allow long messages. The amount of data transferred by the protocols is the same and depends on the structure of the shortest-path spanning-tree; it is no more, and sometimes significantly less, than the cost of constructing the shortest-path tree.

Cowen gave a universal compact routing algorithm with a stretch factor of three and table-size of O(n2/3log4/3n) based on a simple and practical model. (The table-size is later improved to O(n1/2log3/2n).) This paper considers, using the same model, how the necessary table-size differs if the stretch factor must be less than three. It is shown that: (i) There is a routing algorithm with a stretch factor of two whose table-size is (n -+ 2)log n. (ii) There is a network for which any routing algorithm that follows the model and with a stretch factor of less than three needs a table-size of (n - 2)log n in at least one node. Thus, we can only reduce roughly an additive log n (i.e., table-entries) from the trivial table-size of n log n which obviously enables shortest-path routing. Furthermore it turns out that we can reduce only an additive log n (i.e., only one table-entry) from the trivial n log n if we have to achieve a stretch factor of less than two. Thus the algorithm (i) is (roughly) tight both in its stretch factor and in its table-size.

The availability of a low cost hardware has increased the development of distributed systems, by making then more and more accessible. In order to optimize the resources allocation on the distributed systems, some load balancing algorithms have been proposed. These algorithms distribute the application loads over the environment computers, make homogeneous the occupation of the whole environment and increase the application performance. This equal distribution prevents certain computers to get overloaded, to the detriment of the idleness of the other ones. This article proposes and analyzes the TLBAGrid, a load balancing algorithm for Grid computing environments.

Group mutual exclusion is an interesting generalization of the mutual exclusion problem. This problem was introduced by Joung, and some algorithms for the problem have been proposed by incorporating mutual exclusion algorithms. Group mutual exclusion occurs naturally in a situation where a resource can be shared by processes of the same group, but not by processes of a different group. It is also called the congenial talking philosophers problem. In this paper we propose two algorithms based on ticket orders for the group mutual exclusion problem on the asynchronous shared memory model. These algorithms are some modifications of the Bakery algorithm. They satisfy lockout freedom and a high degree of concurrency performance. Each of these algorithms uses single-writer shared variables together with two multi-writer shared variables that are never concurrently written. One of these algorithms has another desirable property, called smooth admission. By this property, during the period that the resource is occupied by the leader (called the chair), a process wishing to join the same group as the leader's group can be granted use of the resource in constant time.

This paper presents a strictly time- and communication-optimal distributed sorting algorithm in a line network. A strictly time-optimal distributed sorting algorithm in a line network has already been designed. However, its communication complexity is not strictly optimal and it seems to be difficult to extend it to other problems, such as that related to multiple elements in a process, and also the dynamic sorting problem where the number of elements each process should have as its solution is not the same as that in the initial state. Therefore, the algorithm in this paper was designed by an alternative approach to make it strictly time- and communication-optimal. Moreover, an extension to the dynamic sorting problem is described.

In this paper, we present the results of a comparative analysis of Atomic Broadcast algorithms. The analysis was done by using an analytical method to compare the performance of five different classes of Atomic Broadcast algorithms. The five classes of Atomic Broadcast algorithms are determined by the mechanisms used by the algorithms to define the delivery order. To evaluate the performance of algorithms, the analysis relies on contention-aware metrics to provide a measure for both their latency and their throughput. The results thus obtained yield interesting insight into the performance tradeoffs of different Atomic Broadcast algorithms, thus providing helpful information to algorithms and systems designers.

This paper defines the distributed arrangement selection problem in a line network in a distributed context and describes the design of a strictly-time-optimal algorithm which solves the problem with a limited local memory space. The problem is regarded as a combined distributed sorting and k-selection problem, namely a problem of sorting elements that are not larger than the kth minimum element in predetermined processes. The algorithm also provides a solution to a resource allocation problem in a line network in a strictly-optimal time.

We propose two simple algorithms based on bounded tickets for the mutual exclusion problem on the asynchronous single-writer/multi-reader shared memory model. These algorithms are modifications of the Bakery algorithm. An unattractive property of the Bakery algorithm is that the size of its shared memory is unbounded. Initially we design a provisional algorithm based on bounded tickets. It guarantees mutual exclusion in the case where a certain condition is satisfied. To remove the condition, we use an additional process that does not correspond to any user. The algorithm with the additional process is a lockout-free mutual exclusion algorithm on the asynchronous single-writer/multi-reader shared memory model. We then modify this algorithm to reduce the shared memory size with the cost of using another additional process. The maximum waiting time using each of the algorithms proposed in this paper is bounded by (n-1)c+O(nl), where n is the number of users, l is an upper bound on the time between two successive atomic steps, and c is an upper bound on the time that any user spends using the resource. The shared memory size needed by the first algorithm and the second algorithm are (n+1)(1+log (4n)) bits and n(1+log (4n-4))+2 bits, respectively.

When a randomized algorithm elects a leader on anonymous networks, initial information (which is called in general initial condition in this paper) of some sort is always needed. In this paper, we study common properties of initial conditions that enable a randomized algorithm to elect a leader. In the previous papers, the author introduced the notion of transformation between initial conditions using distributed algorithms. By using this notion of transformation, we investigate the property of initial conditions for the leader election. We define that an initial condition C is p(N)-complete if there exists some randomized algorithm that elects a leader with probability p(N) on any size N network satisfying C. We show that we can divide p(N)-completeness into four types as follows. 1. p(N)=1: For any 1-complete initial conditions, there exists a deterministic distributed algorithm that can compute the size of the network for any initial information satisfying the initial condition. 2. inf p(N) >0: For any p(N)-complete initial conditions with inf p(N) >0, there exists a deterministic distributed algorithm that can compute an upper-bound for the size of the network for any initial information satisfying the initial condition. 3. inf p(N) converges to 0: The set of p(N)-complete initial conditions varies depending on the decrease rate of p(N). 4. p(N) decreases exponentially: Any initial condition is regarded as p(N)-complete.

We call a network an anonymous network, if each vertex of the network is given no ID's. For distributed algorithms for anonymous networks, solvable problems depend strongly on the given initial conditions. In the past, initial conditions have been investigated, for example, by computation given the number of vertices as the initial condition, and in terms of what initial condition is needed to elect a leader. In this paper, we study the relations among initial conditions. To achieve this task, we define the relation between initial conditions A and B (denoted by A B) as the relation that some distributed algorithm can compute B on any network satisfying A. Then we show the following property of this relation among initial conditions. The relation is a partial order with respect to equivalence classes. Moreover, over initial conditions, it induces a lattice which has maxima and minima, and contains an infinite number of elements. On the other hand, we give new initial conditions k-LEADER and k-COLOR. k-LEADER denotes the initial condition that gives special condition only to k vertices. k-COLOR denotes the initial condition that divides the vertices into k groups. Then we investigate the property of the relation among these initial conditions.

A distributed system is said to be self-stabilizing if it converges to some legitimate state from an arbitrary state in a finite number of steps. The number of steps required for convergence is usually referred to as the stabilization time, and its reduction is one of the main performance issues in the design of self-stabilizing systems. In this paper, we propose an automated method for computing the stabilization time. The method uses Boolean functions to represent the state space in order to assuage the state explosion problem, and computes the stabilization time by manipulating the Boolean functions. To demonstrate the usefulness of the method, we apply it to the analysis of existing self-stabilizing algorithms. The results show that the method can perform stabilization time analysis very fast, even when an underlying state space is very huge.

We investigate possibility of fault-tolerant and self-stabilizing protocols (ftss protocols) using an unreliable failure detector. Our main contribution is (1) to newly introduce k-accuracy of an unreliable failure detector, (2) to show that k-accuracy of a failure detector is necessary for any ftss k-group consensus protocol, and (3) to present three ftss k-group consensus protocols using a k-accurate and weakly complete failure detector under the read/write daemon on complete networks and on (n-k+1)-connected networks, and under the central daemon on complete networks.

For many military and civilian large-scale, real-world systems of interest, data are first acquired asynchronously, i. e. at irregular intervals of time, at geographically-dispersed sites, processed utilizing decision-making algorithms, and the processed data then disseminated to other appropriate sites. The term real-world refers to systems under computer control that relate to everyday life and are beneficial to the society in the large. The traditional approach to such problems consists of designing a central entity which collects all data, executes a decision making algorithm sequentially to yield the decisions, and propagates the decisions to the respective sites. Centralized decision making algorithms are slow and highly vulnerable to natural and artificial catastrophes. Recent literature includes successful asynchronous, distributed, decision making algorithm designs wherein the local decision making at every site replaces the centralized decision making to achieve faster response, higher reliability, and greater accuracy of the decisions. Two key issues include the lack of an approach to synthesize asynchronous, distributed, decision making algorithms, for any given problem, and the absence of a comparative analysis of the quality of their decisions. This paper proposes MFAD, a Mathematical Framework for Asynchronous, Distributed Systems, that permits the description of centralized decision-making algorithms and facilities the synthesis of distributed decision-making algorithms. MFAD is based on the Kohn-Nerode distributed hybrid control paradigm. It has been a belief that since the centralized control gathers every necessary data from all entities in the system and utilizes them to compute the decisions, the decisions may be "globally" optimal. In truth, however, as the frequency of the sensor data increases and the environment gets larger, dynamic, and more complex, the decisions are called into question. In the distributed decision-making system, the centralized decision-making is replaced by those of the constituent entities that aim at minimizing a Lagrangian, i. e. a local, non-negative cost criterion, subject to the constraints imposed by the global goal. Thus, computations are carried out locally, utilizing locally obtained dataand appropriate information that is propagated from other sites. It is hypothesized that with each entity engaged in optimizing its individual behavior, asynchronously, concurrently, and independent of other entities, the distributed system will approach "global" optimal behavior. While it does not claim that such algorithms may be synthesized for all centralized real-world systems, this paper implements both the centralized and distributed paradigms for a representative military battlefield command, control, and communication (C3) problem. It also simulates them on a testbed of a network of workstations for a comparative performance evaluation of the centralized and decentralized paradigms in the MFAD framework. While the performance results indicate that the decentralized approach consistently outperforms the centralized scheme, this paper aims at developing a quantitative evaluation of the quality of decisions under the decentralized paradigm. To achieve this goal, it introduces a fundamental concept, embodied through a hypothetical entity termed "Perfect Global Optimization Device (PGOD)," that generates perfect or ideal decisions. PGOD possesses perfect knowledge, i. e. the exact state information of every entity of the entire system, at all times, unaffected by delay. PGOD utilizes the same decision-making algorithm as the centralized paradigm and generates perfect globally-optimal decisions which, though unattainable, provide a fundamental and absolute basis for comparing the quality of decisions. Simulation results reveal that the quality of decisions in the decentralized paradigm are superior to those of the centralized approach and that they approach PGOD's decisions.

Asynchronous, distributed, decision-making (ADDM) systems constitute a special class of distributed problems and are characterized as large, complex systems wherein the principal elements are the geographically-dispersed entities that communicate among themselves, asynchronously, through message passing and are permitted autonomy in local decision-making. A fundamental property of ADDM systems is stability that refers to their behavior under representative perturbations to their operating environments, given that such systems are intended to be real, complex, and to some extent, mission critical systems, and are subject to unexpected changes in their operating conditions. ADDM systems are closely related to autonomous decentralized systems (ADS) in the principal elements, the difference being that the characteristics and boundaries of ADDM systems are defined rigorously. This paper introduces the concept of stability in ADDM systems and proposes an intuitive yet practical and usable definition that is inspired by those used in Control Systems and Physics. A comprehensive stability analysis on an accurate simulation model will provide the necessary assurance, with a high level of confidence, that the system will perform adequately. An ADDM system is defined as a stable system if it returns to a steady-state in finite time, following perturbation, provided that it is initiated in a steady-state. Equilibrium or steady-state is defined through placing bounds on the measured error in the system. Where the final steady-state is equivalent to the initial one, a system is referred to as strongly stable. If the final steady-state is potentially worse then the initial one, a system is deemed marginally stable. When a system fails to return to steady-state following the perturbation, it is unstable. The perturbations are classified as either changes in the input pattern or changes in one or more environmental characteristics of the system such as hardware failures. Thus, the key elements in the study of stability include steady-state, perturbations, and stability. Since the development of rigorous analytical models for most ADDM systems is difficult, if not impossible, the definitions of the key elements, proposed in this paper, constitute a general framework to investigate stability. For a given ADDM system, the definitions are based on the performance indices that must be judiciously identified by the system architect and are likely to be unique. While a comprehensive study of all possible perturbations is too complex and time consuming, this paper focuses on a key subset of perturbations that are important and are likely to occur with greater frequency. To facilitate the understanding of stability in representative real-world systems, this paper reports the analysis of two basic manifestations of ADDM systems that have been reported in the literature --(i) a decentralized military command and control problem, MFAD, and (ii) a novel distributed algorithm with soft reservation for efficient scheduling and congestion mitigation in railway networks, RYNSORD. Stability analysis of MFAD and RYNSORD yields key stable and unstable conditions.

This paper studies the "usefulness" of initial conditions for distributed algorithms on anonymous networks. In the literature, several initial conditions such as making one vertex a leader, giving the number of vertex to each vertices, and so on, have been considered. In this paper, we study a relation between the initial condition by considering transformation algorithm from one initial condition to another. For such transformation algorithms, we consider in this paper, both deterministic and randomized distributed algorithms. For each deterministic and randomized transformation type, we show that the relation induces an infinite lattice structure among equivalence classes of initial conditions.

Distributed computation has attracted considerable attention and large-scale distributed systems have been designed and developed. A distributed system inherently has possibility of fault tolerance because of its redundancy. Thus, a great deal of investigation has been made to design fault-tolerant distributed algorithms. This paper introduces two promising paradigms, self-stabilization and wait-freedom, for designing fault-tolerant distributed algorithms and discusses some subjects important from the point of view of algorithm engineering.

A coterie is a set of quorums such that any two quorums intersect each other, and is used in a quorum based algorithm for solving the mutual exclusion problem. The availability of a coterie is the probability that the algorithm (adopting the coterie) tolerates process and/or link failures. Constructing an optimal coterie in terms of the availability is therefore important from the view of fault tolerance, but unfortunately, even calculating the availability is known to be #P-hard. Recently Harada and Yamashita proposed several heuristic methods for improving the availability of a coterie. This letter first evaluates their performance and then proposes a practical method for constructing a semi-optimal coterie by using one of the heuristic methods as a main component.