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45
RKleene: A HighPerformance DivideandConquer Algorithm for the AllPair Shortest Path for Densely Connected Networks
, 2007
"... We propose a novel divideandconquer algorithm for the solution of the allpair shortestpath problem for directed and dense graphs with no negative cycles. We propose RKleene, a compact and inplace recursive algorithm inspired by Kleene’s algorithm. RKleene delivers a better performance than p ..."
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We propose a novel divideandconquer algorithm for the solution of the allpair shortestpath problem for directed and dense graphs with no negative cycles. We propose RKleene, a compact and inplace recursive algorithm inspired by Kleene’s algorithm. RKleene delivers a better performance than previous algorithms for randomly generated graphs represented by highly dense adjacency matrices, in which the matrix components can have any integer value. We show that RKleene, unchanged and without any machine tuning, yields consistently between 1/7 and 1/2 of the peak performance running on five very different uniprocessor systems.
On the Power of BFS to Determine a Graph's Diameter
 Networks
, 2003
"... this paper, we show that, in some cases, the full power of LBFS is not required and that other variations of Breadth First Search (BFS) suffice. The restricted graph classes that are amenable to this approach all have a small constant upper bound on the maximumsized cycle that may appear as an indu ..."
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Cited by 9 (0 self)
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this paper, we show that, in some cases, the full power of LBFS is not required and that other variations of Breadth First Search (BFS) suffice. The restricted graph classes that are amenable to this approach all have a small constant upper bound on the maximumsized cycle that may appear as an induced subgraph. We show that, on graphs that have no induced cycle of size greater than k, BFS finds an estimate of the diameter that is no worse than diam(G) # #k/2#. 2003 Wiley Periodicals, Inc
Fast and accurate estimation of shortest paths in large graphs
 In Proceedings of Conference on Information and Knowledge Management (CIKM
, 2010
"... Computing shortest paths between two given nodes is a fundamental operation over graphs, but known to be nontrivial over large diskresident instances of graph data. While a numberoftechniquesexistfor answeringreachabilityqueries and approximating node distances efficiently, determining actual short ..."
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Computing shortest paths between two given nodes is a fundamental operation over graphs, but known to be nontrivial over large diskresident instances of graph data. While a numberoftechniquesexistfor answeringreachabilityqueries and approximating node distances efficiently, determining actual shortest paths (i.e. the sequence of nodes involved) is often neglected. However, in applications arising in massive online social networks, biological networks, and knowledge graphs it is often essential to find out many, if not all, shortest paths between two given nodes. In this paper, we address this problem and present a scalable sketchbased index structure that not only supports estimation of node distances, but also computes corresponding shortest paths themselves. Generating the actual path information allows for further improvements to the estimation accuracy of distances (and paths), leading to nearexact shortestpath approximations in real world graphs. We evaluate our techniques – implemented within a fully functional RDF graph database system – over large realworld social and biological networks of sizes ranging from tens of thousand to millions of nodes and edges. Experiments on several datasets show that we can achieve query response times providing several orders of magnitude speedup over traditional path computations while keeping the estimation errors between 0 % and 1 % on average.
Wellseparated pair decomposition for the unitdisk graph metric and its applications
 SIAM Journal on Computing
, 2003
"... Abstract. We extend the classic notion of wellseparated pair decomposition [10] to the unitdisk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unitdisk graph metric of n points in the plane and for any constant c ≥ 1, there ex ..."
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Abstract. We extend the classic notion of wellseparated pair decomposition [10] to the unitdisk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unitdisk graph metric of n points in the plane and for any constant c ≥ 1, there exists a cwellseparated pair decomposition with O(n log n) pairs, and the decomposition can be computed in O(n log n) time. We also show that for the unitball graph metric in k dimensions where k ≥ 3, there exists a cwellseparated pair decomposition with O(n 2−2/k) pairs, and the bound is tight in the worst case. We present the application of the wellseparated pair decomposition in obtaining efficient algorithms for approximating the diameter, closest pair, nearest neighbor, center, median, and stretch factor, all under the unitdisk graph metric. Keywords Well separated pair decomposition, Unitdisk graph, Approximation algorithm
Compact roundtrip routing with topologyindependent node names
 In Proceedings of the TwentySecond Annual Symposium on Principles of Distributed Computing
, 2003
"... This paper presents compact roundtrip routing schemes with local tables of size Õ( √ n) and stretch 6 for any directed network with arbitrary edge weights; and with local tables of size Õ(ǫ−1 n 2/k) and stretch min((2 k/2 − 1)(k + ǫ),16k 2 + 8k − 8), for any directed network with polynomiallysized ..."
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Cited by 7 (0 self)
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This paper presents compact roundtrip routing schemes with local tables of size Õ( √ n) and stretch 6 for any directed network with arbitrary edge weights; and with local tables of size Õ(ǫ−1 n 2/k) and stretch min((2 k/2 − 1)(k + ǫ),16k 2 + 8k − 8), for any directed network with polynomiallysized edges, both in the topologyindependent nodename model. 1 These are the first topologyindependent results that apply to routing in directed networks.
Fast Computation of Empirically Tight Bounds for the Diameter of Massive Graphs
"... The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones producing approximate values, have too high a time and/or space com ..."
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The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones producing approximate values, have too high a time and/or space complexity to be used in such cases. We propose here a new approach relying on very simple and fast algorithms that compute (upper and lower) bounds for the diameter. We show empirically that, on various realworld cases representative of complex networks studied in the literature, the obtained bounds are very tight (and even equal in some cases). This leads to rigorous and very accurate estimations of the actual diameter in cases which were previously untractable in practice. 1 Context. Throughout the paper, we consider a connected undirected unweighted graph G = (V, E) with n = V  vertices and m = E  edges. We denote by d(u, v) the distance between u and v in G, by ecc(v) = maxu d(v, u) the eccentricity of v in G, and by D = maxu,v d(u, v) = maxvecc(v) the diameter of G.
On the ComparisonAddition Complexity of AllPairs Shortest Paths
 In Proc. 13th Int'l Symp. on Algorithms and Computation (ISAAC'02
, 2002
"... We present an allpairs shortest path algorithm for arbitrary graphs that performs O(mn log (m; n)) comparison and addition operations, where m and n are the number of edges and vertices, resp., and is Tarjan's inverseAckermann function. Our algorithm eliminates the sorting bottleneck inherent in a ..."
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Cited by 6 (5 self)
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We present an allpairs shortest path algorithm for arbitrary graphs that performs O(mn log (m; n)) comparison and addition operations, where m and n are the number of edges and vertices, resp., and is Tarjan's inverseAckermann function. Our algorithm eliminates the sorting bottleneck inherent in approaches based on Dijkstra's algorithm, and for graphs with O(n) edges our algorithm is within a tiny O(log (n; n)) factor of optimal. Our algorithm can be implemented to run in polynomial time (granted, a large polynomial). We leave open the problem of providing an efficient implementation.
Highly Parallel Sparse MatrixMatrix Multiplication
, 2010
"... Generalized sparse matrixmatrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on ..."
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Generalized sparse matrixmatrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on twodimensional block distribution of sparse matrices where serial sections use a novel hypersparse kernel for scalability. We give a stateoftheart MPI implementation of one of our algorithms. Our experiments show scaling up to thousands of processors on a variety of test scenarios.
Soundness of resourceconstrained workflow nets
 In ICATPN
, 2005
"... Abstract. We study concurrent processes modelled as workflow Petri nets extended with resource constraints. We define a behavioural correctness criterion called soundness: given a sufficient initial number of resources, all cases in the net are guaranteed to terminate successfully, no matter which s ..."
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Abstract. We study concurrent processes modelled as workflow Petri nets extended with resource constraints. We define a behavioural correctness criterion called soundness: given a sufficient initial number of resources, all cases in the net are guaranteed to terminate successfully, no matter which schedule is used. We give a necessary and sufficient condition for soundness and an algorithm that checks it.
A Continuous Query System for Dynamic Route Planning
"... Abstract—In this paper, we address the problem of answering continuous route planning queries over a road network, in the presence of updates to the delay (cost) estimates of links. A simple approach to this problem would be to recompute the best path for all queries on arrival of every delay update ..."
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Abstract—In this paper, we address the problem of answering continuous route planning queries over a road network, in the presence of updates to the delay (cost) estimates of links. A simple approach to this problem would be to recompute the best path for all queries on arrival of every delay update. However, such a naive approach scales poorly when there are many users who have requested routes in the system. Instead, we propose two new classes of approximate techniques – Kpaths and proximity measures to substantially speed up processing of the set of designated routes specified by continuous route planning queries in the face of incoming traffic delay updates. Our techniques work through a combination of precomputation of likely good paths and by avoiding complete recalculations on every delay update, instead only sending the user new routes when delays change significantly. Based on an experimental evaluation with 7,000 drives from real taxi cabs, we found that the routes delivered by our techniques are within 5 % of the best shortest path and have run times an order of magnitude or less compared to a naive approach. I.