L. Arge, G. Brodal, and L. Toma. On external-memory MST, SSSP and multi-way planar graph separation. In Proc. 8th Scandinavian Workshop on Algorithmic Theory, volume 1851 of LNCS, pages 433--447. Springer Verlag, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....yields an improved semi external BFS algorithm for sparse directed Eulerian graphs (Section 8) Finally, Section 9 provides some concluding remarks and open problems. 2 Previous Work and New Results Previous Work. I O efficient algorithms for graph traversal have been considered in, e.g. [1, 3, 4, 7 14]. In the following we will only discuss results related to BFS. The currently fastest BFS algorithm for general undirected graphs [14] requires (n sort(m) I Os. The best bound known for directed EM BFS is O(minfn M ; n ) log 2 g) I Os [7 9] This also yields an O(n ) I O ....

....tree for the connected component C s that contains the source node s. Observe that C s can be obtained with the deterministic connectedcomponents algorithm of [14] using O( 1 log log(D B n=m) sort(n m) I Os. The same amount of I O suffices to compute a (minimum) spanning tree T s for C s [3]. After T s has been built, the preprocessing constructs an Euler Tour around T s using a constant number of sort and scan steps [8] Then the tour is broken at the source node s; the elements of the resulting list can be stored in consecutive order using the deterministic list ranking algorithm ....

L. Arge, G. Brodal, and L. Toma. On external-memory MST, SSSP and multi-way planar graph separation. In Proc. 8th Scand. Workshop on Algorithmic Theory, volume 1851 of LNCS, pages 433--447. Springer, 2000.

....O(n m n Sort(n) I Os for BFS [4] and O(n m B log n B ) I Os for DFS and SSSP [3] Better algorithms are known for special graph classes, see [6] for an overview. Furthermore, there is an O(Sort(n) I O algorithm for SSSP on undirected planar graphs G with bounded degree [2]. However, it requires a BFStree for G as part of the input. New Results. We show how a modi cation of the BFS algorithm of Munagala and Ranade [4] can take advantage of a redundant graph representation. For arbitrary undirected graphs with maximumnode degree d B we obtain an O( n log ....

....85, 66123 Saarbr ucken, Germany. www.mpi sb.mpg.de umeyer Work partially supported by the IST Programme of the EU under contract number IST 1999 14186 (ALCOM FT) for an arbitrary parameter 0 1=2. The extended graph representation can be built within the above bounds. Using results of [2] we obtain the same bound for BFS, DFS and SSSP on undirected planar graphs with arbitrary node degrees. 2 Preliminaries Let L(t) denote the set of nodes in the BFS level t, and let jL(t)j be the number of nodes in L(t) The BFS algorithm of Munagala and Ranade [4] builds L(t) as follows: let A ....

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L. Arge, G. Brodal, and L. Toma. On external-memory MST, SSSP and multi-way planar graph separation. In Proc. 8th Scand.Workshop on Alg. Theory, LNCS. Springer, 2000.

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L. Arge, G. Brodal, and L. Toma. On external-memory MST, SSSP and multi-way planar graph separation. In Proc. 8th Scandinavian Workshop on Algorithmic Theory, volume 1851 of LNCS, pages 433--447. Springer Verlag, 2000.

.... For undirected graphs, an improved O(V sort(E) BFS algorithm has been developed [30] The best known algorithms for computing the connected components and the minimal spanning forest of a general undirected graph both use O(sort(E) log 2 log 2 ( E ) or O(V sort(E) memory transfers [30, 11]. Both these algorithms are improvements of algorithms developed in [1, 19, 28] 1.2 Our results The main result of this paper is an optimal cache oblivious priority queue. Our structure supports insert, delete, and ) amortized memory transfers and O(log N) amortized computation time it is ....

....We now consider algorithms for computing the minimal spanning forest (MSF) of an undirected weighted graph. In the I O model, a string of algorithms have been developed for the problem, culminating in an algorithm using O(sort(E) log 2 log 2 ( memory transfers developed by Arge et al. [19, 1, 28, 11]. This algorithm consists of two phases [11] In the rst phase an edge contraction algorithm inspired by PRAM MSF algorithms is used [20, 22] After the number of vertices has been reduced to O(E=B) a modi ed version of Prim s algorithm is then used in the second phase. Using our ....

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L. Arge, G. S. Brodal, and L. Toma. On external memory MST, SSSP and multi-way planar graph separation. In Proc. Scandinavian Workshop on Algorithms Theory, LNCS 1851, pages 433-447, 2000.

....external priority queue. Using the buffer tree technique on a tournament tree, Kumar and Schwabe [107] developed a priority queue supporting update operations in O( 1 B log N B ) I Os. They also showed how to use their structure in several efficient external graph algorithms (see e. g [2, 7, 18, 22, 27, 46, 59, 81, 97, 107, 110, 111, 116, 118, 122, 142, 156] for other results on external graph algorithms and data structures) Note that if the priority of an element is known, an update operation can be performed in O( 1 B log M=B N B ) I Os on a buffer tree using a delete and an insert operation. 4 3 sided planar range searching In internal ....

L. Arge, G. S. Brodal, and L. Toma. On external memory MST, SSSP and multiway planar graph separation. In Proc. Scandinavian Workshop on Algorithms Theory, LNCS 1851, pages 433--447, 2000.

....well on dense graphs. In this paper we consider an important class of sparse graphs, namely undirected embedded planar graphs. This class is restricted enough to hope for more efficient algorithms than for arbitrary sparse graphs. Several such algorithms have indeed been obtained recently [3, 15]. We develop an improved DFS algorithm for planar graphs and show how planar DFS can be reduced to planar BFS. Since several other problems on planar graphs have also been shown to be reducible to BFS, this provides further evidence that in external memory BFS is among the hardest problems on ....

....space, for any 0 fl 1=2. Further improved algorithms have been developed for special classes of planar graphs. For trees, O(sort(N) I O algorithms are known for both BFS and DFS as well as for Euler tour computation, expression tree evaluation, topological sorting, and several other problems [6, 8, 3]. BFS and DFS can also be solved in O(sort(N) I Os on outerplanar graphs [13] and on k outerplanar graphs [14] Developing O(sort(N) I O DFS and BFS algorithms for arbitrary planar graphs remains a challenging open problem. 1.2 Our Results The contribution of this paper is two fold. In Sec. 2 ....

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L. Arge, G. S. Brodal, and L. Toma. On external memory MST, SSSP and multiway planar graph separation. In Proc. Scandinavian Workshop on Algorithms Theory, LNCS 1851, pages 433--447, 2000.

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L. Arge, G. Brodal, and L. Toma. On external memory MST, SSSP and multi-way planar graph separation. In 7th Scandinavian Workshop on Algorithm Theory, volume 1851 of LNCS, pages 433--447. Springer, 2000.

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