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On External Memory MST, SSSP and Multiway Planar Graph Separation (Extended Abstract)
, 2000
"... Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain ..."
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Cited by 33 (11 self)
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Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain open. In this paper we develop improved algorithms for the problem of computing a minimum spanning tree of a general graph G = (V; E), as well as new algorithms for the single source shortest paths and the multiway graph separation problems on planar graphs.
I/OEfficient Algorithms for Problems on Gridbased Terrains (Extended Abstract)
 In Proc. Workshop on Algorithm Engineering and Experimentation
, 2000
"... Lars Arge Laura Toma Jeffrey Scott Vitter Center for Geometric Computing Department of Computer Science Duke University Durham, NC 277080129 Abstract The potential and use of Geographic Information Systems (GIS) is rapidly increasing due to the increasing availability of massive amoun ..."
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Cited by 31 (14 self)
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Lars Arge Laura Toma Jeffrey Scott Vitter Center for Geometric Computing Department of Computer Science Duke University Durham, NC 277080129 Abstract The potential and use of Geographic Information Systems (GIS) is rapidly increasing due to the increasing availability of massive amounts of geospatial data from projects like NASA's Mission to Planet Earth. However, the use of these massive datasets also exposes scalability problems with existing GIS algorithms. These scalability problems are mainly due to the fact that most GIS algorithms have been designed to minimize internal computation time, while I/O communication often is the bottleneck when processing massive amounts of data.
On externalmemory MST, SSSP and multiway planar graph separation
 In Proc. 8th Scandinavian Workshop on Algorithmic Theory, volume 1851 of LNCS
, 2000
"... Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain open ..."
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Cited by 24 (2 self)
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Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/Oefficient graph algorithms have been developed, a number of fundamental problems still remain open. In this paper we develop an improved algorithm for the problem of computing a minimum spanning tree of a general graph, as well as new algorithms for the single source shortest paths and the multiway graph separation problems on planar graphs.
Efficient query processing on spatial networks
 In Proceedings of the 13th ACM International Symposium on Advances in Geographic Information Systems
, 2005
"... A framework for determining the shortest path and the distance between every pair of vertices on a spatial network is presented. The framework, termed SILC, uses path coherence between the shortest path and the spatial positions of vertices on the spatial network, thereby, resulting in an encoding t ..."
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Cited by 23 (12 self)
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A framework for determining the shortest path and the distance between every pair of vertices on a spatial network is presented. The framework, termed SILC, uses path coherence between the shortest path and the spatial positions of vertices on the spatial network, thereby, resulting in an encoding that is compact in representation and fast in path and distance retrievals. Using this framework, a wide variety of spatial queries such as incremental nearest neighbor searches and spatial distance joins can be shown to work on datasets of locations residing on a spatial network of sufficiently large size. The suggested framework is suitable for both main memory and diskresident datasets. Categories and Subject Descriptors
The optimal sequenced route query
 VLDB Journal
, 2005
"... Several variations of nearest neighbor (NN) query have been investigated by the database community. However, realworld applications often result in the formulation of new variations of the NN problem demanding new solutions. In this paper, we study an unexploited and novel form of NN queries named O ..."
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Cited by 13 (1 self)
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Several variations of nearest neighbor (NN) query have been investigated by the database community. However, realworld applications often result in the formulation of new variations of the NN problem demanding new solutions. In this paper, we study an unexploited and novel form of NN queries named Optimal Sequenced Route (OSR) query in both vector and metric spaces. OSR strives to find a route of minimum length starting from a given source location and passing through a number of typed locations in a specific sequence imposed on the types of the locations. We first transform the OSR problem into a shortest path problem on a large planar graph. We show that a classic shortest path algorithm such as Dijkstra’s is impractical for most realworld scenarios. Therefore, we propose LORD, a light thresholdbased iterative algorithm, that utilizes various thresholds to filter out the locations that cannot be in the optimal route. Then we propose RLORD, an extension of LORD which uses Rtree to examine the threshold values more efficiently. Finally, LORD and RLORD are not applicable in metric spaces, hence we propose another approach that progressively issues NN queries on different point types to construct the optimal route for the OSR query. Our extensive experiments using both realworld and synthetic datasets verify that our algorithms significantly outperform the Dijkstrabased approach in terms of processing time (up to two orders of magnitude) and required workspace (up to 90 % reduction on average). 1.
Bulk Synchronous Parallel Algorithms for the External Memory Model
, 2002
"... Blockwise access to data is a central theme in the design of efficient external memory (EM) algorithms. A second important issue, when more than one disk is present, is fully parallel disk I/O. In this paper we present a simple, deterministic simulation technique which transforms certain Bulk Synchr ..."
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Cited by 9 (2 self)
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Blockwise access to data is a central theme in the design of efficient external memory (EM) algorithms. A second important issue, when more than one disk is present, is fully parallel disk I/O. In this paper we present a simple, deterministic simulation technique which transforms certain Bulk Synchronous Parallel (BSP) algorithms into efficient parallel EM algorithms. It optimizes blockwise data access and parallel disk I/O and, at the same time, utilizes multiple processors connected via a communication network or shared memory. We obtain new improved parallel EM algorithms for a large number of problems including sorting, permutation, matrix transpose, several geometric and GIS problems including threedimensional convex hulls (twodimensional Voronoi diagrams), and various graph problems. We show that certain parallel algorithms known for the BSP model can be used to obtain EM algorithms that meet well known I/O complexity lower bounds for various problems, including sorting.
I/Oefficient strong connectivity and depthfirst search for directed planar graphs
 In Proceedings of the 44th IEEE Symposium on Foundations of Computer Science
, 2003
"... We present the first I/Oefficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simplepath 2 3separator, and computing a depthfirst spanning (DFS) tree. Our algorithms for the first two problems perform O(sort(N ..."
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Cited by 6 (6 self)
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We present the first I/Oefficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simplepath 2 3separator, and computing a depthfirst spanning (DFS) tree. Our algorithms for the first two problems perform O(sort(N)) I/Os, where N = V + E and sort(N) = Θ((N/B)log M/B (N/B)) is the number of I/Os required to sort N elements. The DFSalgorithm performs O(sort(N)log(N/M)) I/Os, where M is the number of elements that fit into main memory. 1.
I/OEfficient Planar Separators and Applications
, 2001
"... We present a new algorithm to compute a subset S of vertices of a planar graph G whose removal partitions G into O(N/h) subgraphs of size O(h) and with boundary size O( p h) each. The size of S is O(N= p h). Computing S takes O(sort(N)) I/Os and linear space, provided that M 56hlog² B. Together with ..."
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Cited by 3 (1 self)
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We present a new algorithm to compute a subset S of vertices of a planar graph G whose removal partitions G into O(N/h) subgraphs of size O(h) and with boundary size O( p h) each. The size of S is O(N= p h). Computing S takes O(sort(N)) I/Os and linear space, provided that M 56hlog² B. Together with recent reducibility results, this leads to O(sort(N)) I/O algorithms for breadthfirst search (BFS), depthfirst search (DFS), and single source shortest paths (SSSP) on undirected embedded planar graphs. Our separator algorithm does not need a BFS tree or an embedding of G to be given as part of the input. Instead we argue that "local embeddings" of subgraphs of G are enough.
Exact Distance Oracles for Planar Graphs
, 2010
"... We provide the first linearspace data structure with provable sublinear query time for exact pointtopoint shortest path queries in planar graphs. We prove that for any planar graph G with nonnegative arc lengths and for any ɛ> 0 there is a data structure that supports exact shortest path and dist ..."
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Cited by 3 (2 self)
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We provide the first linearspace data structure with provable sublinear query time for exact pointtopoint shortest path queries in planar graphs. We prove that for any planar graph G with nonnegative arc lengths and for any ɛ> 0 there is a data structure that supports exact shortest path and distance queries in G with the following properties: the data structure can be created in time O(n lg(n) lg(1/ɛ)), the space required is O(n lg(1/ɛ)), and the query time is O(n 1/2+ɛ). Previous data structures by Fakcharoenphol and Rao (JCSS’06), Klein, Mozes, and Weimann (TransAlg’10), and Mozes and WulffNilsen (ESA’10) with query time O(n 1/2 lg 2 n) use space at least Ω(n lg n / lg lg n). We also give a construction with a more general tradeoff. We prove that for any integer S ∈ [n lg n, n 2], we can construct in time Õ(S) a data structure of size O(S) that answers distance queries in O(nS −1/2 lg 2.5 n) time per query. Cabello (SODA’06) gave a comparable construction for the smaller range S ∈ [n 4/3 lg 1/3 n, n 2]. For the range S ∈ (n lg n, n 4/3 lg 1/3 n), only data structures of size O(S) with query time O(n 2 /S) had been known (Djidjev, WG’96). Combined, our results give the best query times for any shortestpath data structure for planar graphs with space S = o(n 4/3 lg 1/3 n). As a consequence, we also obtain an algorithm that computes k–many distances in planar graphs in time O((kn) 2/3 (lg n) 2 (lg lg n) −1/3 + n(lg n) 2 / lg lg n). 1