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Reports tagged with reachability:
TR01-092 | 2nd October 2001
Till Tantau

A Note on the Complexity of the Reachability Problem for Tournaments

Deciding whether a vertex in a graph is reachable from another
vertex has been studied intensively in complexity theory and is
well understood. For common types of graphs like directed graphs,
undirected graphs, dags or trees it takes a (possibly
nondeterministic) logspace machine to decide the reachability
problem, and ... more >>>

TR03-077 | 4th September 2003
Till Tantau

Logspace Optimisation Problems and their Approximation Properties

This paper introduces logspace optimisation problems as
analogues of the well-studied polynomial-time optimisation
problems. Similarly to them, logspace
optimisation problems can have vastly different approximation
properties, even though the underlying existence and budget problems
have the same computational complexity. Numerous natural problems
are presented that exhibit such a varying ... more >>>

TR06-035 | 19th January 2006
Till Tantau

The Descriptive Complexity of the Reachability Problem As a Function of Different Graph Parameters

The reachability problem for graphs cannot be described, in the
sense of descriptive complexity theory, using a single first-order
formula. This is true both for directed and undirected graphs, both
in the finite and infinite. However, if we restrict ourselves to
graphs in which a certain graph parameter is fixed ... more >>>

TR09-029 | 3rd April 2009
Fabian Wagner, Thomas Thierauf

Reachability in K_{3,3}-free Graphs and K_5-free Graphs is in Unambiguous Log-Space

Revisions: 1

We show that the reachability problem for directed graphs
that are either K_{3,3}-free or K_5-free
is in unambiguous log-space, UL \cap coUL.
This significantly extends the result of Bourke, Tewari, and Vinodchandran
that the reachability problem for directed planar graphs
is in UL \cap coUL.

Our algorithm decomposes ... more >>>

TR09-049 | 5th May 2009
Derrick Stolee, Chris Bourke, N. V. Vinodchandran

A log-space algorithm for reachability in planar DAGs with few sources

Designing algorithms that use logarithmic space for graph reachability problems is fundamental to complexity theory. It is well known that for general directed graphs this problem is equivalent to the NL vs L problem. For planar graphs, the question is not settled. Showing that the planar reachability problem is NL-complete ... more >>>

TR10-154 | 8th October 2010
Derrick Stolee, N. V. Vinodchandran

Space-Efficient Algorithms for Reachability in Surface-Embedded Graphs

We consider the reachability problem for a certain class of directed acyclic graphs embedded on surfaces. Let ${\cal G}(m,g)$ be the class of directed acyclic graphs with $m = m(n)$ source vertices embedded on a surface (orientable or non-orientable) of genus $g = g(n)$. We give a log-space reduction that ... more >>>

TR14-035 | 13th March 2014
Diptarka Chakraborty, A. Pavan, Raghunath Tewari, N. V. Vinodchandran, Lin Yang

New Time-Space Upperbounds for Directed Reachability in High-genus and $H$-minor-free Graphs.

We obtain the following new simultaneous time-space upper bounds for the directed reachability problem.
(1) A polynomial-time,
$\tilde{O}(n^{2/3}g^{1/3})$-space algorithm for directed graphs embedded on orientable surfaces of genus $g$. (2) A polynomial-time, $\tilde{O}(n^{2/3})$-space algorithm for all $H$-minor-free graphs given the tree decomposition, and (3) for $K_{3, 3}$-free and ... more >>>

TR14-071 | 7th May 2014
Tetsuo Asano, David Kirkpatrick, Kotaro Nakagawa, Osamu Watanabe

O(sqrt(n))-Space and Polynomial-time Algorithm for the Planar Directed Graph Reachability Problem

We show an O(sqrt(n))-space and polynomial-time algorithm for solving the planar directed graph reachability problem. Imai et al. showed in CCC 2013 that the problem is solvable in O(n^{1/2+eps})-space and polynomial-time by using separators for planar graphs, and it has been open whether the space bound can be improved to ... more >>>

TR16-155 | 10th October 2016
Vaibhav Krishan, Nutan Limaye

Isolation Lemma for Directed Reachability and NL vs. L

In this work we study the problem of efficiently isolating witnesses for the complexity classes NL and LogCFL, which are two well-studied complexity classes contained in P. We prove that if there is a L/poly randomized procedure with success probability at least 2/3 for isolating an s-t path in a ... more >>>

TR18-106 | 30th May 2018
Chetan Gupta, Vimalraj Sharma, Raghunath Tewari

Reachability in $O(\log n)$ Genus Graphs is in Unambiguous

Revisions: 1

Given the polygonal schema embedding of an $O(log n)$ genus graph $G$ and two vertices
$s$ and $t$ in $G$, we show that deciding if there is a path from $s$ to $t$ in $G$ is in unambiguous
logarithmic space.

more >>>

TR19-039 | 12th March 2019
Eric Allender, Archit Chauhan, Samir Datta, Anish Mukherjee

Planarity, Exclusivity, and Unambiguity

Comments: 1

We provide new upper bounds on the complexity of the s-t-connectivity problem in planar graphs, thereby providing additional evidence that this problem is not complete for NL. This also yields a new upper bound on the complexity of computing edit distance. Building on these techniques, we provide new upper bounds ... more >>>

TR21-027 | 24th February 2021
Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh Saxena, Zhao Song, Huacheng Yu

Almost Optimal Super-Constant-Pass Streaming Lower Bounds for Reachability

We give an almost quadratic $n^{2-o(1)}$ lower bound on the space consumption of any $o(\sqrt{\log n})$-pass streaming algorithm solving the (directed) $s$-$t$ reachability problem. This means that any such algorithm must essentially store the entire graph. As corollaries, we obtain almost quadratic space lower bounds for additional fundamental problems, including ... more >>>

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