Abstract
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 important restricted version of the reachability problem, where the input graph is planar. Planar reachability is hard for L and is contained in NL but is not known to be NL-complete or contained in L. Allender et al. [2009] showed that reachability for graphs embedded on the torus is logspace-reducible to the planar case. We generalize this result to graphs embedded on a fixed surface of arbitrary genus.
- Allender, E., Barrington, D. A. M., Chakraborty, T., Datta, S., and Roy, S. 2009. Planar and grid graph reachability problems. Theory Comput. Syst. 45, 4, 675--723. Google Scholar
Digital Library
- Allender, E. and Mahajan, M. 2004. The complexity of planarity testing. Inf. Comput. 189, 1, 117--134. Google Scholar
Digital Library
- Bourke, C., Tewari, R., and Vinodchandran, N. V. 2009. Directed planar reachability is in unambiguous log-space. ACM Trans. Comput. Theory 1, 1, 1--17. Google Scholar
Digital Library
- Jakoby, A., Liśkiewicz, M., and Reischuk, R. 2006. Space efficient algorithms for directed series-parallel graphs. J. Algor. 60, 2, 85--114. Google Scholar
Digital Library
- Mohar, B. and Thomassen, C. 2001. Graphs on Surfaces. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD.Google Scholar
- Nisan, N. and Ta-Shma, A. 1995. Symmetric logspace is closed under complement. Chicago J. Theoret. Comput. Sci., Article 1, 13pp.Google Scholar
- Reingold, O. 2008. Undirected connectivity in log-space. J. ACM 55, 4, Art. 17, 24. Google Scholar
Digital Library
- Stolee, D., Bourke, C., and Vinodchandran, N. V. 2009. A log-space algorithm for reachability in planar dags with few sources. Tech. rep. 49, Electronic Colloquium on Computational Complexity.Google Scholar
- Thierauf, T. and Wagner, F. 2009. Reachability in K3, 3-free graphs and K5-free graphs is in unambiguous log-space. Tech. rep. 29, Electronic Colloquium on Computational Complexity.Google Scholar
Index Terms
Logspace Reduction of Directed Reachability for Bounded Genus Graphs to the Planar Case
Recommendations
Directed Planar Reachability Is in Unambiguous Log-Space
We make progress in understanding the complexity of the graph reachability problem in the context of unambiguous logarithmic space computation; a restricted form of nondeterminism. As our main result, we show a new upper bound on the directed planar ...
The Bidimensional Theory of Bounded-Genus Graphs
Bidimensionality provides a tool for developing subexponential fixed-parameter algorithms for combinatorial optimization problems on graph families that exclude a minor. This paper extends the theory of bidimensionality for graphs of bounded genus (...
Planar and Grid Graph Reachability Problems
Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea SorbiWe study the complexity of restricted versions of s-t-connectivity, which is the standard complete problem for $\mathsf{NL}$. In particular, we focus on different classes of planar graphs, of which grid graphs are an important special case. Our main ...






Comments