Erratum and addendum to “A linear time algorithm for finding all hinge vertices of a permutation graph” [Information Processing Letters 59 (2) (1996) 103-107]

This note points out and corrects an error in the algorithm proposed in [Ting-Yem Ho, Yue-Li Wang and Ming-Tsan Juan, A linear time algorithm for finding all hinge vertices of a permutation graph, Information Processing Letters 59 (2) (1996) 103-107].     

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.     

An efficient distributed algorithm for generating and updating multicast trees

As group applications are becoming widespread, efficient network utilization becomes a growing concern. Multicast transmission represents a necessary lower network service for the wide diffusion of new multimedia network applications. Multicast transmission may use network resources more efficiently than multiple point-to-point messages; however, creating optimal multicast trees (Steiner Tree Problem in networks) is prohibitively expensive. This paper proposes a distributed algorithm for the heuristic solution of the Steiner Tree Problem, allowing the construction of effective distribution trees using a coordination protocol among the network nodes. Furthermore, we propose a novel distributed technique for dynamically updating the multicast tree. The approach proposed has been implemented and extensively tested both in simulation, and on experimental networks. Performance evaluation indicates that the distributed algorithm performs as well as the centralized version, providing good levels of convergence time and communication complexity.     

An algorithm for privacy-preserving distributed user statistics

In this paper, we propose a privacy-preserving method to determine the number of distinct users who connected to one or more entry points of a distributed Internet service with multiple service operators. The problem is motivated by the anonymization network Tor, and the difficulties that arise when aiming to estimate the number of Tor users. We present a way to perform distributed user counting with accurate estimates and a high level of privacy protection, based on a probabilistic data structure. We start from a relatively naive approach, and analyze the level of privacy protection that it provides. Subsequently, we improve on this baseline mechanism, building upon the gained insights. In order to assess the privacy properties of the discussed techniques, we use a novel probabilistic analysis approach which compares an attacker’s a priori and a posteriori knowledge.     

An improved algorithm for finding the median distributively

Given two processes, each having a total-ordered set ofn elements, we present a distributed algorithm for finding median of these 2n elements using no more than logn +O(logn) messages, but if the elements are distinct, only logn +O(1) messages will be required. The communication complexity of our algorithm is better than the previously known result which takes 2 logn messages.     

An efficient distributed randomized algorithm for solving large dense symmetric indefinite linear systems

Randomized algorithms are gaining ground in high-performance computing applications as they have the potential to outperform deterministic methods, while still providing accurate results. We propose a randomized solver for distributed multicore architectures to efficiently solve large dense symmetric indefinite linear systems that are encountered, for instance, in parameter estimation problems or electromagnetism simulations. The contribution of this paper is to propose efficient kernels for applying random butterfly transformations and a new distributed implementation combined with a runtime (PaRSEC) that automatically adjusts data structures, data mappings, and the scheduling as systems scale up. Both the parallel distributed solver and the supporting runtime environment are innovative. To our knowledge, the randomization approach associated with this solver has never been used in public domain software for symmetric indefinite systems. The underlying runtime framework allows seamless data mapping and task scheduling, mapping its capabilities to the underlying hardware features of heterogeneous distributed architectures. The performance of our software is similar to that obtained for symmetric positive definite systems, but requires only half the execution time and half the amount of data storage of a general dense solver.     

Improved algorithm for finding next-to-shortest paths

We study the problem of finding the next-to-shortest paths in a weighted undirected graph. A next-to-shortest (u,v)-path is a shortest (u,v)-path amongst (u,v)-paths with length strictly greater than the length of the shortest (u,v)-path. The first polynomial algorithm for this problem was presented in [I. Krasikov, S.D. Noble, Finding next-to-shortest paths in a graph, Inform. Process. Lett. 92 (2004) 117-119]. We improve the upper bound from O(n³m) to O(n³).     

An optimal distributed algorithm for finding articulation points in a network

This paper presents a distributed algorithm for finding the articulation points in an n node communication network represented by a connected undirected graph. For a given graph if the deletion of a node splits the graph into two or more components then that node is called an articulation point. The output of the algorithm is available in a distributed manner, i.e., when the algorithm terminates each node knows whether it is an articulation point or not. It is shown that the algorithm requires O(n) messages and O(n) units of time and is optimal in communication complexity to within a constant factor.     

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 simple local 3-approximation algorithm for vertex cover

We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required.     

A self-stabilizing algorithm for constructing weakly connected minimal dominating sets

This paper presents a new distributed self-stabilizing algorithm for the weakly connected minimal dominating set problem. It assumes a self-stabilizing algorithm to compute a breadth-first tree. Using an unfair distributed scheduler the algorithm stabilizes in at most O(nmA) moves, where A is the number of moves to construct a breadth-first tree. All previously known algorithms required an exponential number of moves.     

Reconfigurable distributed storage for dynamic networks

This paper presents a new algorithm for implementing a reconfigurable distributed shared memory in an asynchronous dynamic network. The algorithm guarantees atomic consistency (linearizability) in all executions in the presence of arbitrary crash failures of the processing nodes, message delays, and message loss. The algorithm incorporates a classic quorum-based algorithm for read/write operations, and an optimized consensus protocol, based on Fast Paxos for reconfiguration, and achieves the design goals of: (i) allowing read and write operations to complete rapidly and (ii) providing long-term fault-tolerance through reconfiguration, a process that evolves the quorum configurations used by the read and write operations. The resulting algorithm tolerates dynamism. We formally prove our algorithm to be correct, we present its performance and compare it to existing reconfigurable memories, and we evaluate experimentally the cost of its reconfiguration mechanism.     

An efficient algorithm for minimum feedback vertex sets in rotator graphs

For a rotator graph with n! nodes, Hsu and Lin [C.C. Hsu, H.R. Lin, H.C. Chang, K.K. Lin, Feedback Vertex Sets in Rotator Graphs, in: Lecture Notes in Comput. Sci., vol. 3984, 2006, pp. 158-164] first proposed an algorithm which constructed a feedback vertex set (FVS) with time complexity O(nn−3). In addition, they found that the size of the FVS is n!/3, which was proved to be minimum. In this paper, we present an efficient algorithm which constructs an FVS for a rotator graph in O(n!) time and also obtains the minimum FVS size n!/3. In other words, this algorithm derives the optimal result with linear time complexity in terms of the number of nodes in the rotator graph.     

Improved algorithm for all pairs shortest paths

We present an improved algorithm for all pairs shortest paths. For a graph of n vertices our algorithm runs in O(n³(loglogn/logn)^5/7) time. This improves the best previous result which runs in O(n³(loglogn/logn)^1/2) time.     

An efficient parallel algorithm for finding rectangular duals of plane triangular graphs

We present an efficient parallel algorithm for constructing rectangular duals of plane triangular graphs. This problem finds applications in VLSI design and floor-planning problems. No NC algorithm for solving this problem was previously known. The algorithm takesO(log² n) time withO(n) processors on a CRCW PRAM, wheren is the number of vertices of the graph.This research was supported by NSF Grants CCR-9011214 and CCR-9205982.     

An efficient weighted bi-objective scheduling algorithm for heterogeneous systems

This paper proposes the Makespan and Reliability Cost Driven (MRCD) heuristic, a static scheduling strategy for heterogeneous distributed systems that not only minimizes the makespan, but also maximizes the reliability of the application. The MRCD scheduling decisions are guided by a weighted function that considers both objectives simultaneously, instead of prioritizing one of them. This work also introduces a classification of the solutions produced by weighted bi-objective schedulers to aid users to tune the weighting function such that an appropriate solution can be selected in accordance with their needs. In comparison with the related work, MRCD produced schedules with makespans that were significantly better then those produced by the other strategies at expense of an insignificant deterioration in reliability.     

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.     

An efficient distributed algorithm for constructing small dominating sets

The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NP-complete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the well-known logarithmic approximation result for the closely related set cover problem. We describe and analyze new randomized distributed algorithms for the dominating set problem that run in polylogarithmic time, independent of the diameter of the network, and that return a dominating set of size within a logarithmic factor from optimal, with high probability. In particular, our best algorithm runs in rounds with high probability, where n is the number of nodes, is one plus the maximum degree of any node, and each round involves a constant number of message exchanges among any two neighbors; the size of the dominating set obtained is within of the optimal in expectation and within of the optimal with high probability. We also describe generalizations to the weighted case and the case of multiple covering requirements. Received: January 2002 / Accepted: August 2002 RID="*" ID="*" Supported by NSF CAREER award NSF CCR-9983901 RID="*" ID="*" Supported by NSF CAREER award NSF CCR-9983901     

An incentive-based distributed mechanism for scheduling divisible loads in tree networks

The underlying assumption of Divisible Load Scheduling (DLS) theory is that the processors composing the network are obedient, i.e., they do not “cheat” the scheduling algorithm. This assumption is unrealistic if the processors are owned by autonomous, self-interested organizations that have no a priori motivation for cooperation and they will manipulate the algorithm if it is beneficial to do so. In this paper, we address this issue by designing a distributed mechanism for scheduling divisible loads in tree networks, called DLS-T, which provides incentives to processors for reporting their true processing capacity and executing their assigned load at full processing capacity. We prove that the DLS-T mechanism computes the optimal allocation in an ex post Nash equilibrium. Finally, we simulate and study the mechanism under various network structures and processor parameters.