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44
ExternalMemory Graph Algorithms
, 1995
"... We present a collection of new techniques for designing and analyzing efficient externalmemory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: ffl Proximateneighboring. We present a simple method for der ..."
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Cited by 175 (24 self)
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We present a collection of new techniques for designing and analyzing efficient externalmemory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: ffl Proximateneighboring. We present a simple method for deriving externalmemory lower bounds via reductions from a problem we call the "proximate neighbors" problem. We use this technique to derive nontrivial lower bounds for such problems as list ranking, expression tree evaluation, and connected components. ffl PRAM simulation. We give methods for efficiently simulating PRAM computations in external memory, even for some cases in which the PRAM algorithm is not workoptimal. We apply this to derive a number of optimal (and simple) externalmemory graph algorithms. ffl Timeforward processing. We present a general technique for evaluating circuits (or "circuitlike" computations) in external memory. We also use this in a deterministic list rank...
A Functional Approach to External Graph Algorithms
 Algorithmica
, 1998
"... . We present a new approach for designing external graph algorithms and use it to design simple external algorithms for computing connected components, minimum spanning trees, bottleneck minimum spanning trees, and maximal matchings in undirected graphs and multigraphs. Our I/O bounds compete w ..."
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Cited by 90 (2 self)
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. We present a new approach for designing external graph algorithms and use it to design simple external algorithms for computing connected components, minimum spanning trees, bottleneck minimum spanning trees, and maximal matchings in undirected graphs and multigraphs. Our I/O bounds compete with those of previous approaches. Unlike previous approaches, ours is purely functionalwithout side effectsand is thus amenable to standard checkpointing and programming language optimization techniques. This is an important practical consideration for applications that may take hours to run. 1 Introduction We present a divideandconquer approach for designing external graph algorithms, i.e., algorithms on graphs that are too large to fit in main memory. Our approach is simple to describe and implement: it builds a succession of graph transformations that reduce to sorting, selection, and a recursive bucketing technique. No sophisticated data structures are needed. We apply our t...
I/OComplexity of Graph Algorithms
, 1999
"... We show lower bounds of \Omega\Gamma E V Sort(V )) for the I/Ocomplexity of graph theoretic problems like connected components, biconnected components, and minimum spanning trees, where E and V are the number of edges and vertices in the input graph, respectively. We also present a deterministic O ..."
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Cited by 68 (0 self)
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We show lower bounds of \Omega\Gamma E V Sort(V )) for the I/Ocomplexity of graph theoretic problems like connected components, biconnected components, and minimum spanning trees, where E and V are the number of edges and vertices in the input graph, respectively. We also present a deterministic O( E V Sort(V ) \Delta max(1; log log V BD E )) algorithm for the problem of graph connectivity, where B and D denote respectively the block size and number of disks. Our algorithm includes a breadth first search; this maybe of independent interest. 1 Introduction Data sets of many modern applications are too large to fit into main memory, and must reside on disk. To run such applications efficiently, it is often necessary to explicitly manage disk accesses as a part of the algorithm. In other words, the algorithm must be designed for a model that includes disk, rather than the customary RAM model. Recently, this area has received a lot of attention, and algorithms have been developed for...
Cacheoblivious priority queue and graph algorithm applications
 In Proc. 34th Annual ACM Symposium on Theory of Computing
, 2002
"... In this paper we develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in O ( 1 B logM/B N) amortized memory B transfers, where M and B are the memory and block transfer sizes of any two consecutive levels of a multilevel memory hi ..."
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Cited by 68 (10 self)
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In this paper we develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in O ( 1 B logM/B N) amortized memory B transfers, where M and B are the memory and block transfer sizes of any two consecutive levels of a multilevel memory hierarchy. In a cacheoblivious data structure, M and B are not used in the description of the structure. The bounds match the bounds of several previously developed externalmemory (cacheaware) priority queue data structures, which all rely crucially on knowledge about M and B. Priority queues are a critical component in many of the best known externalmemory graph algorithms, and using our cacheoblivious priority queue we develop several cacheoblivious graph algorithms.
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.
A Fast, Parallel Spanning Tree Algorithm for Symmetric Multiprocessors (SMPs) (Extended Abstract)
, 2004
"... Our study in this paper focuses on implementing parallel spanning tree algorithms on SMPs. Spanning tree is an important problem in the sense that it is the building block for many other parallel graph algorithms and also because it is representative of a large class of irregular combinatorial probl ..."
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Cited by 31 (11 self)
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Our study in this paper focuses on implementing parallel spanning tree algorithms on SMPs. Spanning tree is an important problem in the sense that it is the building block for many other parallel graph algorithms and also because it is representative of a large class of irregular combinatorial problems that have simple and efficient sequential implementations and fast PRAM algorithms, but often have no known efficient parallel implementations. In this paper we present a new randomized algorithm and implementation with superior performance that for the firsttime achieves parallel speedup on arbitrary graphs (both regular and irregular topologies) when compared with the best sequential implementation for finding a spanning tree. This new algorithm uses several techniques to give an expected running time that scales linearly with the number p of processors for suitably large inputs (n> p 2). As the spanning tree problem is notoriously hard for any parallel implementation to achieve reasonable speedup, our study may shed new light on implementing PRAM algorithms for sharedmemory parallel computers. The main results of this paper are 1. A new and practical spanning tree algorithm for symmetric multiprocessors that exhibits parallel speedups on graphs with regular and irregular topologies; and 2. An experimental study of parallel spanning tree algorithms that reveals the superior performance of our new approach compared with the previous algorithms. The source code for these algorithms is freelyavailable from our web site hpc.ece.unm.edu.
A Parallel Algorithm for Computing Minimum Spanning Trees
, 1992
"... We present a simple and implementable algorithm that computes a minimum spanning tree of an undirected weighted graph G = (V, E) of n = V vertices and m = E edges on an EREW PRAM in O(log 3=2 n) time using n+m processors. This represents a substantial improvement in the running time over the ..."
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Cited by 31 (3 self)
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We present a simple and implementable algorithm that computes a minimum spanning tree of an undirected weighted graph G = (V, E) of n = V vertices and m = E edges on an EREW PRAM in O(log 3=2 n) time using n+m processors. This represents a substantial improvement in the running time over the previous results for this problem using at the same time the weakest of the PRAM models. It also implies the existence of algorithms having the same complexity bounds for the EREW PRAM, for connectivity, ear decomposition, biconnectivity, strong orientation, stnumbering and Euler tours problems.
Fast Connected Components Algorithms For The EREW PRAM
 SIAM J. COMPUT
, 1999
"... We present fast and e#cient parallel algorithms for finding the connected components of an undirected graph. These algorithms run on the exclusiveread, exclusivewrite (EREW) PRAM. On a graph with n vertices and m edges, our randomized algorithm runs ..."
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Cited by 26 (3 self)
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We present fast and e#cient parallel algorithms for finding the connected components of an undirected graph. These algorithms run on the exclusiveread, exclusivewrite (EREW) PRAM. On a graph with<F3.492e+05> n<F3.822e+05> vertices and<F3.492e+05> m<F3.822e+05> edges, our randomized algorithm runs in<F3.492e+05><F3.822e+05> O(log<F3.492e+05><F3.822e+05> n) time using<F3.492e+05> (m<F3.822e+05> +<F3.492e+05> n<F2.77e+05><F2.072e+05> 1+#<F3.822e+05><F3.492e+05> )/<F3.822e+05> log<F3.492e+05> n<F3.822e+05> EREW processors (for any fixed<F3.492e+05> # ><F3.822e+05> 0). A variant uses<F3.492e+05> (m<F3.822e+05> +<F3.492e+05><F3.822e+05><F3.492e+05> n)/<F3.822e+05> log<F3.492e+05> n<F3.822e+05> processors and runs in<F3.492e+05><F3.822e+05> O(log<F3.492e+05> n<F3.822e+05> log log<F3.492e+05><F3.822e+05> n) time. A deterministic version of the algorithm runs in<F3.492e+05><F3.822e+05> O(log<F2.77e+05><F2.072e+05><F2.77e+05> 1.5<F3.492e+05><F3.822e+05> n) time using<F3.492e+...
Parallel Algorithms for Hierarchical Clustering and Applications to Split Decomposition and Parity Graph Recognition
 JOURNAL OF ALGORITHMS
, 1998
"... We present efficient (parallel) algorithms for two hierarchical clustering heuristics. We point out that these heuristics can also be applied to solve some algorithmic problems in graphs. This includes split decomposition. We show that efficient parallel split decomposition induces an efficient para ..."
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Cited by 24 (1 self)
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We present efficient (parallel) algorithms for two hierarchical clustering heuristics. We point out that these heuristics can also be applied to solve some algorithmic problems in graphs. This includes split decomposition. We show that efficient parallel split decomposition induces an efficient parallel parity graph recognition algorithm. This is a consequence of the result of [7] that parity graphs are exactly those graphs that can be split decomposed into cliques and bipartite graphs.
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 ..."
Abstract

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.