Journal ArticleDOI
Planar Strong Connectivity Helps in Parallel Depth-First Search
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TLDR
This paper proves that for a strongly connected planar directed graph of size $n$, a depth-first search tree rooted at a specified vertex can be computed in $O(\log^{5}n)$ time with $n/\log{n}$ processors.Abstract:
This paper proves that for a strongly connected planar directed graph of size $n$, a depth-first search tree rooted at a specified vertex can be computed in $O(\log^{5}n)$ time with $n/\log{n}$ processors. Previously, for planar directed graphs that may not be strongly connected, the best depth-first search algorithm runs in $O(\log^{10}n)$ time with $n$ processors. Both algorithms run on a parallel random access machine that allows concurrent reads and concurrent writes in its shared memory, and in case of a write conflict, permits an arbitrary processor to succeed.read more
Citations
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Proceedings ArticleDOI
I/O-efficient strong connectivity and depth-first search for directed planar graphs
Lars Arge,Norbert Zeh +1 more
TL;DR: The first I/O-efficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simple-path 2/3-separator, and computing a depth-first spanning (DFS) tree are presented.
Book ChapterDOI
Fast Universalization of Investment Strategies with Provably Good Relative Returns
TL;DR: In this article, the authors present a general framework for universalizing investment strategies and discuss conditions under which investment strategies are universalizable, including trading strategies that decide positions in individual stocks, and portfolio strategies that allocate wealth among multiple stocks.
Book ChapterDOI
Efficient Parallel Algorithms for Planar st-Graphs
TL;DR: This paper presents efficient parallel algorithms for solving several fundamental problems on planar st-graphs, which include all-pairs shortest paths in weighted planar St-Graphs, single-source shortest path in weightedPlanar layered digraphs, and depth-first search in planarSt- graphs.
Journal ArticleDOI
An optimal parallel algorithm for planar cycle separators
TL;DR: An optimal parallel algorithm for computing a cycle separator of ann-vertex embedded planar undirected graph in O(logn) time on n/logn processors is presented and an improved parallel algorithm is obtained for constructing a depth-first search tree rooted at any given vertex in a connected planar Undirectedgraph.
Journal ArticleDOI
Depth-first search in directed planar graphs, revisited
TL;DR: The problem of computing depth-first search trees in other classes of graphs is considered and the fastest uniform deterministic parallel algorithm for this problem had a runtime of O (log 10 n ) (corresponding to the complexity class AC 10 ⊆ NC 11 ).
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
A separator theorem for planar graphs
TL;DR: In this paper, it was shown that the vertices of a planar graph can be partitioned into three sets A,B,C such that no edge joins a vertex in A with another vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than $2.
Journal ArticleDOI
Depth-first search is inherently sequential
TL;DR: It is shown that this problem, for undirected and directed graphs, is complete in deterministic polynomial time with respect to deterministic log-space reductions.