A O~(n2)\tilde O(n^2) Time-Space Trade-off for Undirected s-t Connectivity

Version 3 makes use of the Metropolis-Hastings walkInternational audienceIn this paper, we make use of the Metropolis-type walks due to Nonaka et al. (2010) to provide a faster solution to the $S$-$T$-connectivity problem in undirected graphs (USTCON). As our main result, we propose a family of randomized algorithms for USTCON which achieves a time-space product of $S\cdot T = \tilde O(n^2)$ in graphs with $n$ nodes and $m$ edges (where the $\tilde O$-notation disregards poly-logarithmic terms). This improves the previously best trade-off of $\tilde O(n m)$, due to Feige (1995). Our algorithm consists in deploying several short Metropolis-type walks, starting from landmark nodes distributed using the scheme of Broder et al. (1994) on a modified input graph. In particular, we obtain an algorithm running in time $\tilde O(n+m)$ which is, in general, more space-efficient than both BFS and DFS. We close the paper by showing how to fine-tune the Metropolis-type walk so as to match the performance parameters (e.g., average hitting time) of the unbiased random walk for any graph, while preserving a worst-case bound of $\tilde O(n^2)$ on cover time

A Compendium of Problems Complete for Symmetric Logarithmic Space

. The paper's main contributions are a compendium of problems that are complete for symmetric logarithmic space (SL), a collection of material relating to SL, a list of open problems, and an extension to the number of problems known to be SL-complete. Complete problems are one method of studying SL, a class for which programming is nonintuitive. Our exposition helps make the class SL less mysterious and more accessible to other researchers. Key words. Completeness, SL, space complexity, symmetric logarithmic space. Subject classifications. 68Q17. 1. Introduction In this paper we describe problems that are logarithmic space many-one complete for symmetric logarithmic space (SL). Our hope in collecting these problems and extending this list is that more insight can be gained about the relationships between the complexity classes deterministic logarithmic space (DL), SL, and nondeterministic logarithmic space (NL). The symmetric Turing machine model introduced by Lewis & Papadimitriou ..

A Compendium of Problems Complete for Symmetric Logarithmic Space

We provide a compendium of problems that are complete for symmetric logarithmic space (SL). Complete problems are one method of studying this class for which programming is nonintuitive. A number of the problems in the list were not previously known to be complete. A list containing a variety of open problems is also given. This work was partially supported by ESPRIT LTR Project no. 20244-ALCOM-IT. y This research partially supported by National Science Foundation grant CCR-9209184, a Fulbright Scholarship Senior Research Award 1995, and a Spanish Fellowship for Scientific and Technical Investigations 1996. 1 Introduction In this paper we describe problems that are logarithmic space many-one complete for symmetric logarithmic space (SL). Our hope in collecting these problems and extending this list is that more insight can be gained about the relationships between the complexity classes deterministic logarithmic space (DL), SL, and nondeterministic logarithmic space (NL). The sy..

A Compendium of problems complete for symmetric logarithmic space

We provide a compendium of problems that are complete for symmetric logarithmic space. Complete problems are one method ofstudying this class for which programming is nonintuitive. A number ofthe problems in the list were not previously known to be complete. Alist containing a variety of open problems is also given