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Efficient Parallel Algorithms for Computing All Pair Shortest Paths in Directed Graphs
, 1997
"... . We present parallel algorithms for computing all pair shortest paths in directed graphs. Our algorithm has time complexity O( f (n)/p + I (n) log n) on the PRAM using p processors, where I (n) is log n on the EREW PRAM, log log n on the CCRW PRAM, f (n) is o(n 3 ). On the randomized CRCW PRAM we a ..."
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. We present parallel algorithms for computing all pair shortest paths in directed graphs. Our algorithm has time complexity O( f (n)/p + I (n) log n) on the PRAM using p processors, where I (n) is log n on the EREW PRAM, log log n on the CCRW PRAM, f (n) is o(n 3 ). On the randomized CRCW PRAM we are able to achieve time complexity O(n 3 /p + log n) using p processors. Key Words. Analysis of algorithms, Design of algorithms, Parallel algorithms, Graph algorithms, Shortest path. 1. Introduction. A number of known algorithms compute the all pair shortest paths in graphs and digraphs with n vertices by using O(n 3 ) operations [D], [Fl], [J]. All these algorithms, however, use at least n1 recursive steps in the worst case and thus require at least the order of n time in their parallel implementation, even if the number of available processors is not bounded. O(n) time and n 2 processor bounds can indeed be achieved, for instance, in the straightforward parallelization of th...
Using StochasticDominance Relationships for Bounding Travel Times in Stochastic Networks
, 1999
"... We consider stochastic networks' in which link travel times are dependent, discrete random variables. We present methods' for computing bounds' on path travel times using stochastic dominance relationships among link travel times, and discuss techniques for controlling tightness of th ..."
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We consider stochastic networks' in which link travel times are dependent, discrete random variables. We present methods' for computing bounds' on path travel times using stochastic dominance relationships among link travel times, and discuss techniques for controlling tightness of the bounds'. We apply these methods' to shortestpath problems, show that the proposed algorithm can provide bounds' on the recommended path, and elaborate on extensions of the algorithm for demonstrating the anytime property.
Graph Generation on GPUs using Dynamic Memory Allocation
"... Abstract — Complex networks are often studied using statistical measurements over many independently generated samples. Irregular data structures such as graphs that involve dynamical memory management and “pointer chasing ” are an important class of application and have attracted recent interest in ..."
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Abstract — Complex networks are often studied using statistical measurements over many independently generated samples. Irregular data structures such as graphs that involve dynamical memory management and “pointer chasing ” are an important class of application and have attracted recent interest in the form of the Graph500 benchmark formulation. The generation of simulated sample network graphs and measurement of their properties can be accelerated using Graphical Processing Units (GPUs) and we discuss some algorithmic approaches using Compute Unified Device Architecture (CUDA). We particularly discuss recent support for dynamic memory allocation within CUDA GPU code and present some performance data for Watts ’ α smallworld network model.
A Routing Approach to Reduce Glitches
"... Glitches (spurious transitions) are common in electronic circuits. In this paper we present a novel approach to reduce dynamic power in FPGAs by reducing glitches during the routing step. This approach involves finding alternative routes for earlyarriving signals, so that signal arrival times at LUT ..."
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Glitches (spurious transitions) are common in electronic circuits. In this paper we present a novel approach to reduce dynamic power in FPGAs by reducing glitches during the routing step. This approach involves finding alternative routes for earlyarriving signals, so that signal arrival times at LUTs are aligned and no glitches are generated. This approach does not require additional circuitry to balance signals as done in previous work, but uses the available programmable routing resources instead. We develop an efficient algorithm to find routes with target delays. Based on this algorithm, we then build a glitchaware router, named GlitchReroute, aiming at reducing dynamic power. To the best of our knowledge, this is the first glitchaware routing algorithm for FPGAs. Experiments show that an average of 23% reduction in glitch power is achieved, which translates into a 9.8 % reduction in dynamic power, compared to the glitchunaware VPR router. Categories and Subject Descriptors
Result Verification Algorithms for Optimization Problems
, 1995
"... In this article we discuss the design of result verification algorithms for optimization problems. In particular, we design timeoptimal result verification algorithms which verify the solution of allpairs shortest paths, maximumflow in a network, and matching problems. We prove that polynomialti ..."
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In this article we discuss the design of result verification algorithms for optimization problems. In particular, we design timeoptimal result verification algorithms which verify the solution of allpairs shortest paths, maximumflow in a network, and matching problems. We prove that polynomialtime verification algorithms for NPcomplete problems do not exist exist, unless P = NP. Result verification problems for most of the NPhard problems are not believed to be in NP. We also consider verification algorithms for approximation algorithms for NPcomplete and NPhard problems. 1 Introduction Consider a program A written to evaluate a function f. In this article we address the issue of being able to verify that the program A works correctly for all inputs i.e., A(x) = f(x) for all inputs x. Most of the approaches to this problem fall under the following broad categories: formal verification, program testing/checking and result verification. Formal verification of an algorithm or pro...
BestPath Planning for Public Transportation Systems
"... The author examines methods for a special class of path planning problems in which the routes are constrained. General search algorithms assume that we can move around in the traffic network freely, so they extend the partial paths from the very last location to each of its neighbors to form mor ..."
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The author examines methods for a special class of path planning problems in which the routes are constrained. General search algorithms assume that we can move around in the traffic network freely, so they extend the partial paths from the very last location to each of its neighbors to form more partial paths. The best partial paths are then selected to expand, unless the selected partial path happens to be a solution. Without proper guidance, this strategy may lead to inefficient planning algorithms when the way one can move around in the networks is constrained. This scenario could happen in public transportation systems where passengers cannot order drivers to change the routes of public buses to meet individual travel needs.
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"... The primary function of navigation system is to provide route search and road guidance for safe driving for drivers. However, the existing route search system provides a simple service that looks up the shortest route using a safe driving DB without considering different road characteristics for the ..."
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The primary function of navigation system is to provide route search and road guidance for safe driving for drivers. However, the existing route search system provides a simple service that looks up the shortest route using a safe driving DB without considering different road characteristics for the safety of the drivers. In order to maintain the safe driving, rather than searching the shortest path, a navigation system, in which the danger areas and/or the dangerous time zones have been considered, is required. Therefore, in this paper we propose a strategy of searching a navigation path to avoid danger areas for safe driving by using the A * algorithm. In the strategy, when evaluating the pathspecific fitness of the navigation nodes, different heuristic weights were assigned to different types of risk areas. In particular, we considered three kinds of danger areas, such as accidentprone sections where accidents occur frequently, school zones, and intersection regions, as well as the time slots when the probability of danger is high. From computer simulation, the results demonstrate that the proposed scheme can provide the way to avoid danger areas on the route searching and
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"... Title: Realtime multicast transmission algorithms for P2P networks ..."
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"... This work shows the design and study of a family of algorithms that solves the multicast routing problem. In this problem, a given node called root has to send information to a certain group of receiving nodes. Although the algorithm can be applied at any level of the protocol stack, this paper stud ..."
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This work shows the design and study of a family of algorithms that solves the multicast routing problem. In this problem, a given node called root has to send information to a certain group of receiving nodes. Although the algorithm can be applied at any level of the protocol stack, this paper studies its performance in the application level. This family of algorithms provides optimal routing tables between nodes belonging to the same multicast group, in such a way that the total transmission time is minimum. The algorithms take benefit from the delay time in the transmission of a message between one peer and another to forward the data to a third peer. Beginnig with a first algorithm, defined to send only one packet, some other algorithms has been described under certain conditions to send more than a packet with the maximum possible cadence and without congestion problems. With this purpose, we have restricted the number of times that the root may send a packet and also the maximum cadence time for the rest of the nodes. Moreover, we have applied mechanisms to guarantee full connectivity.
SmallWorld Grid
, 2005
"... As the Grid matures the problem of resource discovery across communities, where resources now include computational services, is becoming more critical. The number of resources available on a worldwide grid is set to grow exponentially in much the same way as the number of static web pages on the ..."
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As the Grid matures the problem of resource discovery across communities, where resources now include computational services, is becoming more critical. The number of resources available on a worldwide grid is set to grow exponentially in much the same way as the number of static web pages on the WWW. We observe that the worldwide resource discovery problem can be modelled as a slowly evolving verylarge sparsematrix where individual matrix elements represent nodes ’ knowledge of one another. Blocks in the matrix arise where nodes o↵er more than one service. Blocking e↵ects also arise in the identification of subcommunities in the Grid. The linear algebra community has long been aware of suitable representations of large, sparse matrices. However, matrices the size of the worldwide grid potentially number in the billions making dense solutions completely intractable. Distributed nodes will not necessarily have the storage capacity to store the addresses of any significant percentage of the available resources. We discuss ways of modelling this problem in the regime of a slowly changing service base including phenomena such as percolating networks and smallworld network e↵ects.