Distributed Shortest Path Research Articles

DMGA: A Distributed Shortest Path Algorithm for Multistage Graph

The multistage graph problem is a special kind of single-source single-sink shortest path problem. It is difficult even impossible to solve the large-scale multistage graphs using a single machine with sequential algorithms. There are many distributed graph computing systems that can solve this problem, but they are often designed for general large-scale graphs, which do not consider the special characteristics of multistage graphs. This paper proposes DMGA (Distributed Multistage Graph Algorithm) to solve the shortest path problem according to the structural characteristics of multistage graphs. The algorithm first allocates the graph to a set of computing nodes to store the vertices of the same stage to the same computing node. Next, DMGA calculates the shortest paths between any pair of starting and ending vertices within a partition by the classical dynamic programming algorithm. Finally, the global shortest path is calculated by subresults exchanging between computing nodes in an iterative method. Our experiments show that the proposed algorithm can effectively reduce the time to solve the shortest path of multistage graphs.

An Energy-efficient Distributed TDMA Scheduling Algorithm for ZigBee-like Cluster-tree WSNs

The design of Medium Access Control (MAC) protocol for Wireless Sensor Networks (WSNs) with both limited energy consumption and data delivery time is crucial for industrial and control applications. Since Time Division Multiple Access (TDMA) MAC eliminates the collision occurrence and seeks the minimization of the number of time-slots assigned to each node, the energy consumption of the nodes is reduced. Furthermore, with the proper allocation of the time-slots to the nodes, the transmission delay can be significantly reduced. In this article, we propose TDMA scheduling algorithm for Cluster-tree topology WSNs that meets the timeliness and the energy demands. The algorithm adopts an elegant approach that expresses the timing constraints of the data transmissions as an integer multiple of the length of the schedule period. Moreover, since the distributed algorithm is well-suited to the scarce resources of the WSNs, we focus on the distributed methods that allow each cluster to come up with its allocated time-slots. The algorithm is based on graph theory, such as distributed shortest path, distributed topological ordering, and distributed graph coloring algorithms. The efficiency of the algorithm, regarding the elapsed time to construct the schedule and the energy consumption, is evaluated over benchmark instances up to several thousands of nodes.

Distributed Real Time TDMA Scheduling Algorithm for Tree Topology WSNs

In this paper, we address the problem of developing TDMA scheduling algorithm for tree topology WSNs. The data transmissions are organized into periodic data flows that may have opposite directions since they are carrying sensor and actuator values for feedback control. It is required to determine a periodic and collision-free allocation of the time-slots to the sensor nodes such that the end-to-end deadline of each data flow, as given in time units, is satisfied. The objective is to maximize the lifetime of the network by maximizing the time when the nodes are in the sleep mode. However, the longer the time at which the nodes stay in the sleep mode, the harder is to meet the timeliness requirements of the data flows. To solve the TDMA scheduling problem, we have found an elegant approach to express the end-to-end deadline as an integer number of the length of the schedule period. Moreover, since the distributed algorithms, in compassion with the centralized algorithms, well-suit the scarce resources of the WSNs, we focus on the distributed methods that allow each node in the network to come up with its allocated time-slots in the schedule. The proposed algorithm is based on the graph theory algorithms, namely the distributed shortest path and the distributed topological ordering. Furthermore, it falls into the category of the exact algorithms for tree topology with single-collision domain and in the category of the heuristic algorithms for multiple-collision domains tree topology.

Enhancing the Computation of Distributed Shortest Paths on Power-law Networks in Dynamic Scenarios

The problem of finding and keeping updated shortest paths in distributed networks is considered crucial in today's practical applications. In the recent past, there has been a renewed interest in devising new efficient distance-vector algorithms as an attractive alternative to link-state solutions for large-scale Ethernet networks, in which scalability and reliability are key issues or the nodes can have limited storage capabilities. In this paper, we present Distributed Computation Pruning (DCP), a new technique, which can be combined with every distance-vector routing algorithm based on shortest paths, allowing to reduce the total number of messages sent by that algorithm and its space occupancy per node. To check its effectiveness, we combined the new technique with DUAL (Diffuse Update ALgorithm), one of the most popular distance-vector algorithm in the literature, which is part of CISCO's widely used EIGRP protocol, and with the recently introduced LFR (Loop Free Routing) which has been shown to have good performances on real networks. We give experimental evidence that these combinations lead to a significant gain both in terms of number of messages sent and of memory requirements per node.

Distributed production planning using a graph-based negotiation protocol

A distributed model for allocating a single job to be processed through multiple machines and alternative routings so that the job flow time is experimentally shown to reach its minimum is presented. Issues are addressed pertaining to dynamic and fully distributed decision-making for determining the job flow time in a cooperative manner between system agents (i.e. machines and a job), and for selecting a good routing (i.e. a short flow time) for a job when alternative routings are available. Two cases with confirmed jobs and without confirmed jobs are examined. The proposed protocols can deal with job shop scheduling with multiple product types in a sequential manner. The model is developed on the basis of a distributed shortest path algorithm using asynchronous job-initiated protocols. These protocols are examined using object-oriented simulation models and it is shown how the agents converge to the optimal path in a finite time.

Negotiation-based multi-stage production control using distributed shortest path algorithm

This paper addresses a fully distributed negotiation-based model for optimally allocating jobs to be processed through multiple machines and alternative routings so that the sojourn time is minimized as confirmed jobs and alternative machines are considered. In this paper, we restrict our discussion to the case in which only one negotiation is active in the shop floor at any time. We explore issues pertaining to dynamic and fully distributed decision making (i) for deciding job completion time in a cooperative manner between machines and a job, and (ii) for choosing the best routing (having minimum sojourn time) for a job when alternative routings are available. The model is developed on the basis of a distributed shortest path algorithm using a job-initiated negotiation protocol. We prove the convergence property of the protocol to guarantee that the system agents can converge to an optimal solution in a finite time. An aggregated model for tackling alternative machines is also developed.