An O(n&amp;#x00BD;+?)-Space and Polynomial-Time Algorithm for Directed Planar Reachability

Imai, T.; Nakagawa, Kotaro; Pavan, A.; Vinodchandran, N. V.; Watanabe, Osamu

doi:10.1109/ccc.2013.35

Cited by 14 publications

(23 citation statements)

References 16 publications

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“…Asano and Doerr [3] presented an algorithm for grid graphs that uses O(n 1/2+ )-space. Then, Imai et al [20] achieved the similar space bound for planar graphs. Later, Asano et al [4] improved the space bound to Õ(n 1/2 ) for planar graphs.…”

Section: Introductionmentioning

confidence: 84%

“…The notion of vertex separator has been previously exploited in designing memory-constrained algorithms, specifically for Reachability problem. In particular, we point out to the work of Imai et al [20] In [22], Jain and Tewari formalized the connection between Vertex Separator and Reachability problems, that has several consequences. For the sake of completeness, we state their theorem below.…”

Section: Introductionmentioning

confidence: 99%

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Space-Efficient Algorithms for Reachability in Geometric Graphs

Bhore,

Jain

2021

Preprint

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The problem of graph Reachability is to decide whether there is a path from one vertex to another in a given graph. In this paper, we study the Reachability problem on three distinct graph families -intersection graphs of Jordan regions, unit contact disk graphs (penny graphs), and chordal graphs. For each of these graph families, we present space-efficient algorithms for the Reachability problem. In order to obtain these results, we use the vertex separator of these graphs effectively, and design space-efficient algorithms to find such separators. The constructions of the separators presented here can be of independent interest. √ log n) ) space. This result was followed by numerous works on various restricted graph Sujoy Bhore acknowledges support from the Fonds de la Recherche Scientifique-FNRS under Grant no MISU F 6001 1.

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Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Space-Efficient Algorithms for Reachability in Geometric Graphs

Bhore,

Jain

2021

Preprint

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“…Imai et al used a separator construction to solve the reachability problem in planar graphs [9]. A separator is a small set of vertices whose removal disconnects the graph into smaller components.…”

Section: Properties Of the Auxiliary Graphmentioning

confidence: 99%

“…It then used a gadget to transform each subgrid into a planar graph, making the whole of the resultant graph planar. Finally, it used the planar reachability algorithm of Imai et al [9] as a subroutine to get the desired space bound.…”

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confidence: 99%

Grid Graph Reachability

Jain,

Tewari

2019

Preprint

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The reachability problem is to determine if there exists a path from one vertex to another in a graph. Grid graphs are the class of graphs where vertices are present on the lattice points of a two-dimensional grid, and an edge can occur between a vertex and its immediate horizontal or vertical neighbor only.Asano et al. presented the first simultaneous time space bound for reachability in grid graphs by presenting an algorithm that solves the problem in polynomial time and O(n 1/2+ǫ ) space. In 2018, the space bound was improved to Õ(n 1/3 ) by Ashida and Nakagawa.In this paper, we show that reachability in an n vertex grid graph can be decided by an algorithm using O(n 1/4+ǫ ) space and polynomial time simultaneously.

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“…The planar graph reachability problem is in the unambiguous log-space class, UL [5], which is a subclass of NL. Imai et al gave an algorithm using O(n 1/2+ε ) space and polynomial time for the planar graph reachability problem [2,8]. Moreover Asano et al devised a efficient way to control the recursion, and proposed a polynomial time and O( √ n) space algorithm for the planar graph reachability problem [3].…”

Section: Introductionmentioning

confidence: 99%

$\tilde{O}(n^{1/3})$-Space Algorithm for the Grid Graph Reachability Problem

Ashida,

Nakagawa

2018

Preprint

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The directed graph reachability problem takes as input an n-vertex directed graph G = (V, E), and two distinguished vertices s and t. The problem is to determine whether there exists a path from s to t in G. This is a canonical complete problem for class NL. Asano et al. proposed an O( √ n) space 1 and polynomial time algorithm for the directed grid and planar graph reachability problem. The main result of this paper is to show that the directed graph reachability problem restricted to grid graphs can be solved in polynomial time using only O(n 1/3 ) space.

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An O(n½+?)-Space and Polynomial-Time Algorithm for Directed Planar Reachability

Cited by 14 publications

References 16 publications

Space-Efficient Algorithms for Reachability in Geometric Graphs

Space-Efficient Algorithms for Reachability in Geometric Graphs

Grid Graph Reachability

$\tilde{O}(n^{1/3})$-Space Algorithm for the Grid Graph Reachability Problem

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