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Electronic Colloquium on Computational Complexity

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Reports tagged with Logspace:
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 >>>

TR04-100 | 23rd November 2004
Eric Allender, Michael Bauland, Neil Immerman, Henning Schnoor, Heribert Vollmer

The Complexity of Satisfiability Problems: Refining Schaefer's Theorem

Revisions: 1

Schaefer proved in 1978 that the Boolean constraint satisfaction problem for a given constraint language is either in P or is NP-complete, and identified all tractable cases. Schaefer's dichotomy theorem actually shows that there are at most two constraint satisfaction problems, up to polynomial-time isomorphism (and these isomorphism types are ... more >>>

TR05-149 | 7th December 2005
Eric Allender, David Mix Barrington, Tanmoy Chakraborty, Samir Datta, Sambuddha Roy

Grid Graph Reachability Problems

Revisions: 1

We study the complexity of restricted versions of st-connectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since
* reachability on grid graphs is logspace-equivalent to reachability in general planar digraphs, and
* reachability on certain classes of grid graphs gives ... more >>>

TR06-130 | 27th September 2006
Tanmoy Chakraborty, Samir Datta

One-input-face MPCVP is Hard for L, but in LogDCFL

A monotone planar circuit (MPC) is a Boolean circuit that can be
embedded in a plane, and that has only AND and OR
gates. Yang showed that the one-input-face
monotone planar circuit value problem (MPCVP) is in NC^2, and
Limaye et. al. improved the bound to ... more >>>

TR07-024 | 5th March 2007
Laszlo Egri, Benoit Larose, Pascal Tesson

Symmetric Datalog and Constraint Satisfaction Problems in Logspace

We introduce symmetric Datalog, a syntactic restriction of linear
Datalog and show that its expressive power is exactly that of
restricted symmetric monotone Krom SNP. The deep result of
Reingold on the complexity of undirected
connectivity suffices to show that symmetric Datalog queries can be
evaluated in logarithmic space. We ... more >>>

TR09-049 | 5th May 2009
Derrick Stolee, Chris Bourke, Vinodchandran Variyam

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 >>>

TR09-050 | 28th May 2009
Jan Kyncl, Tomas Vyskocil

Logspace reduction of directed reachability for bounded genus graphs to the planar case

Directed reachability (or briefly reachability) is the following decision problem: given a directed graph G and two of its vertices s,t, determine whether there is a directed path from s to t in G. Directed reachability is a standard complete problem for the complexity class NL. Planar reachability is an ... more >>>

TR10-062 | 7th April 2010
Michael Elberfeld, Andreas Jakoby, Till Tantau

Logspace Versions of the Theorems of Bodlaender and Courcelle

Bodlaender's Theorem states that for every $k$ there is a linear-time algorithm that decides whether an input graph has tree width~$k$ and, if so, computes a width-$k$ tree composition. Courcelle's Theorem builds on Bodlaender's Theorem and states that for every monadic second-order formula $\phi$ and for
every $k$ there is ... more >>>

TR11-009 | 21st January 2011
Samir Datta, Gautam Prakriya

Planarity Testing Revisited

Planarity Testing is the problem of determining whether a given graph is planar while planar embedding is the corresponding construction problem.
The bounded space complexity of these problems has been determined to be Logspace by Allender and Mahajan with the aid of Reingold's result . Unfortunately, the algorithm is quite ... more >>>

TR12-032 | 4th April 2012
Sebastian Kuhnert, Johannes Köbler, Osamu Watanabe

Interval graph representation with given interval and intersection lengths

We consider the problem of finding interval representations of graphs that additionally respect given interval lengths and/or pairwise intersection lengths, which are represented as weight functions on the vertices and edges, respectively. Pe'er and Shamir proved that the problem is NP-complete if only the former are given [SIAM J. Discr. ... more >>>

TR12-126 | 23rd September 2012
Shiva Kintali, Sinziana Munteanu

Computing Bounded Path Decompositions in Logspace

We present a logspace algorithm to compute path decompositions of bounded pathwidth graphs, thus settling its complexity. Prior to our work, the best known upper bound to compute such decompositions was linear time. We also show that deciding if the pathwidth of a graph is at most a given constant ... more >>>

TR13-064 | 22nd April 2013
Anat Ganor, Ran Raz

Space Pseudorandom Generators by Communication Complexity Lower Bounds

Revisions: 1

In 1989, Babai, Nisan and Szegedy [BNS92] gave a construction of a pseudorandom generator for logspace, based on lower bounds for multiparty communication complexity. The seed length of their pseudorandom generator was $2^{\Theta(\sqrt n)}\,\,\,$, because the best lower bounds for multiparty communication complexity are relatively weak. Subsequently, pseudorandom generators for ... more >>>

TR16-120 | 1st August 2016
Dean Doron, Amir Sarid, Amnon Ta-Shma

On approximating the eigenvalues of stochastic matrices in probabilistic logspace

Revisions: 1

Approximating the eigenvalues of a Hermitian operator can be solved
by a quantum logspace algorithm. We introduce the problem of
approximating the eigenvalues of a given matrix in the context of
classical space-bounded computation. We show that:

- Approximating the second eigenvalue of stochastic operators (in a
certain range of ... 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 >>>

TR17-036 | 22nd February 2017
Dean Doron, Francois Le Gall, Amnon Ta-Shma

Probabilistic logarithmic-space algorithms for Laplacian solvers

A recent series of breakthroughs initiated by Spielman and Teng culminated in the construction of nearly linear time Laplacian solvers, approximating the solution of a linear system $L x=b$, where $L$ is the normalized Laplacian of an undirected graph. In this paper we study the space complexity of the problem.
more >>>

TR19-095 | 18th July 2019
Chetan Gupta, Rahul Jain, Vimal Raj Sharma, Raghunath Tewari

Unambiguous Catalytic Computation

The catalytic Turing machine is a model of computation defined by Buhrman, Cleve,
Kouck, Loff, and Speelman (STOC 2014). Compared to the classical space-bounded Turing
machine, this model has an extra space which is filled with arbitrary content in addition
to the clean space. In such a model we study ... more >>>

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