Constant Queue Route on a Mesh

Packet routing is an important problem in parallel computation since a single step of inter-processor communication can be thought of as a packet routing task. In this paper we present an optimal algorithm for packet routing on a mesh-connected computer. Two important criteria for judging a routing algorithm will be 1) its run time, i.e., the number of parallel steps it takes for the last packet to reach its destination, and 2) its queue size, i.e., the maximum number of packets that any node will have to store at any time during routing. We present a 2n - 2 step routing algorithm for an n x n mesh that requires a queue size of only 58. The previous best known result is a routing algorithm with the same time bound but with a queue size of 672. The time bound of 2n - 2 is optimal. A queue size of 672 is rather large for practical use. We believe that the queue size of our algorithm is practical. The improvement in the queue size is possible due to (from among other things) a new 3s + o(s) sorting algorithm for an s x s mesh

The Network Improvement Problem for Equilibrium Routing

In routing games, agents pick their routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average delay have received substantial attention, including network tolls, Stackelberg routing, and edge removal. A related approach with arguably greater practical relevance is that of making investments in improvements to the edges of the network, so that, for a given investment budget, the average delay at equilibrium in the improved network is minimized. This problem has received considerable attention in the literature on transportation research and a number of different algorithms have been studied. To our knowledge, none of this work gives guarantees on the output quality of any polynomial-time algorithm. We study a model for this problem introduced in transportation research literature, and present both hardness results and algorithms that obtain nearly optimal performance guarantees. - We first show that a simple algorithm obtains good approximation guarantees for the problem. Despite its simplicity, we show that for affine delays the approximation ratio of 4/3 obtained by the algorithm cannot be improved. - To obtain better results, we then consider restricted topologies. For graphs consisting of parallel paths with affine delay functions we give an optimal algorithm. However, for graphs that consist of a series of parallel links, we show the problem is weakly NP-hard. - Finally, we consider the problem in series-parallel graphs, and give an FPTAS for this case. Our work thus formalizes the intuition held by transportation researchers that the network improvement problem is hard, and presents topology-dependent algorithms that have provably tight approximation guarantees.Comment: 27 pages (including abstract), 3 figure

Optimal Routing in two parallel Queues with exponential service times

In this paper we investigate the problem of the effective computation of the optimal routing sequence in a queuing system made of two queues with exponential service time in parallel. We first show that the optimal policy (minimizing the expected waiting time) is a Sturmian sequence and we establish several qualitative properties of this policy (monotonicity, continuity, convexity) Then, we propose an algorithm to compute the optimal routing sequence. We address the issues of time complexity as well as numerical stability of this algorithm. We then run an extensive set of experiments which show several interesting features of the optimal policy with apparent discontinuities and a fractal behavior

A multipopulation parallel genetic simulated annealing based QoS routing and wavelength assignment integration algorithm for multicast in optical networks

Copyright @ 2008 Elsevier B.V. All rights reserved.In this paper, we propose an integrated Quality of Service (QoS) routing algorithm for optical networks. Given a QoS multicast request and the delay interval specified by users, the proposed algorithm can find a flexible-QoS-based cost suboptimal routing tree. The algorithm first constructs the multicast tree based on the multipopulation parallel genetic simulated annealing algorithm, and then assigns wavelengths to the tree based on the wavelength graph. In the algorithm, routing and wavelength assignment are integrated into a single process. For routing, the objective is to find a cost suboptimal multicast tree. For wavelength assignment, the objective is to minimize the delay of the multicast tree, which is achieved by minimizing the number of wavelength conversion. Thus both the cost of multicast tree and the user QoS satisfaction degree can approach the optimal. Our algorithm also considers load balance. Simulation results show that the proposed algorithm is feasible and effective. We also discuss the practical realization mechanisms of the algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1, the National Natural Science Foundation of China under Grant nos. 60673159 and 70671020, the National High-Tech Research and Development Plan of China under Grant no. 2006AA01Z214, Program for New Century Excellent Talents in University, and the Key Project of Chinese Ministry of Education under Grant no. 108040

On Optimal Placements of Processors in Tori Networks

Two and three dimensional k-tori are among the most used topologies in the design of new parallel computers. Traditionally (with the exception of the Tera parallel computer), these networks have been used as fully-populated networks, in the sense that every routing node in the topology is subjected to message injection. However, fully-populated tori and meshes exhibit a theoretical throughput which degrades as the network size increases. In addition, the performance of those networks is sensitive to link faults. In contrast, multistage networks (that are partially populated) scale well with the network size. We propose to add slackness in fully-populated tori by reducing the number of processors and we study optimal fault-tolerant routing strategies for the resulting interconnections. The key concept that we study is the average link load in an interconnection network with a given placement and a routing algorithm, where a placement is the subset of the nodes in the interconnection network that are attached to processors. Reducing the load on the links by the choice of a placement and a routing algorithm leads to improvements in both the performance and the fault tolerance of the communication system. Our main contribution is the construction of optimal placements for 2 and 3-dimensional k-tori networks and their corresponding routing algorithms. Those placements yield a linear (in the number of processors) link load and are of optimal size

A Parallel Monte-Carlo Tree Search-Based Metaheuristic For Optimal Fleet Composition Considering Vehicle Routing Using Branch & Bound

In this paper, a Monte-Carlo Tree Search (MCTS)-based metaheuristic is developed that guides a Branch & Bound (B&B) algorithm to find the globally optimal solution to the heterogeneous fleet composition problem while considering vehicle routing. Fleet Size and Mix Vehicle Routing Problem with Time Windows (FSMVRPTW). The metaheuristic and exact algorithms are implemented in a parallel hybrid optimization algorithm where the metaheuristic rapidly finds feasible solutions that provide candidate upper bounds for the B&B algorithm which runs simultaneously. The MCTS additionally provides a candidate fleet composition to initiate the B&B search. Experiments show that the proposed approach results in significant improvements in computation time and convergence to the optimal solution.Comment: Submitted to the IEEE Intelligent Vehicles Symposium 202

Cross-layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks

This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models

Multistage interconnection networks : improved routing algorithms and fault tolerance

Multistage interconnection networks for use by multiprocessor systems are optimal in terms of the number of switching element, but the routing algorithms used to set up these networks are suboptimal in terms of time. The network set-up time and reliability are the major factors to affect the performance of multistage interconnection networks. This work improves routing on Benes and Clos networks as well as the fault tolerant capability. The permutation representation is examined as well as the Clos and Benes networks. A modified edge coloring algorithm is applied to the regular bipartite multigraph which represents a Clos network. The looping and parallel looping algorithms are examined and a modified Tree-Connected Computer is adopted to execute a bidirectional parallel looping algorithm for Benes networks. A new fault tolerant Clos network is presented