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Electronic Colloquium on Computational Complexity

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Reports tagged with connectivity:
TR05-148 | 6th December 2005
Eric Allender, Samir Datta, Sambuddha Roy

The Directed Planar Reachability Problem

Revisions: 1

We investigate the s-t-connectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspace-reducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to ... more >>>

TR06-094 | 29th July 2006
Parikshit Gopalan, Phokion G. Kolaitis, Elitza Maneva, Christos H. Papadimitriou

The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies

Revisions: 1

Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered around the structure and connectivity of the solution space. Motivated by this work, we study structural and connectivity-related properties of the space of solutions ... more >>>

TR14-037 | 21st March 2014
Hamidreza Jahanjou, Eric Miles, Emanuele Viola

Succinct and explicit circuits for sorting and connectivity

We study which functions can be computed by efficient circuits whose gate connections are very easy to compute. We give quasilinear-size circuits for sorting whose connections can be computed by decision trees with depth logarithmic in the length of the gate description. We also show that NL has NC$^2$ circuits ... more >>>

TR15-101 | 15th June 2015
Patrick Scharpfenecker

On the structure of Solution-Graphs for Boolean Formulas

Revisions: 2

In this work we extend the study of solution graphs and prove that for boolean formulas in a class called CPSS, all connected components are partial cubes of small dimension, a statement which was proved only for some cases in [Schwerdtfeger 2013]. In contrast, we show that general Schaefer formulas ... more >>>

TR18-048 | 11th March 2018
Ofer Grossman, Yang P. Liu

Reproducibility and Pseudo-Determinism in Log-Space

A curious property of randomized log-space search algorithms is that their outputs are often longer than their workspace. This leads to the question: how can we reproduce the results of a randomized log space computation without storing the output or randomness verbatim? Running the algorithm again with new random bits ... more >>>

TR18-129 | 13th July 2018
Jelani Nelson, Huacheng Yu

Optimal Lower Bounds for Distributed and Streaming Spanning Forest Computation

Revisions: 1

We show optimal lower bounds for spanning forest computation in two different models:

* One wants a data structure for fully dynamic spanning forest in which updates can insert or delete edges amongst a base set of $n$ vertices. The sole allowed query asks for a spanning forest, which the ... more >>>

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