David A. Mix Barrington, Chi-Jen Lu, Peter Bro Miltersen, Sven Skyum  Home/Search
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Abstract: We show that searching a width k maze is complete for \Pi k , i.e., for the k'th level of the AC 0 hierarchy. Equivalently, st-connectivity for width k grid graphs is complete for \Pi k . As an application, we show that there is a data structure solving dynamic st-connectivity for constant width grid graphs with time bound O(log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools. 1 Introduction Blum ... (Update)
Context of citations to this paper: More
.... for very narrow graphs: It is known that the reachability problem for grid graphs of constant width can be solved in time O(log log n) by [2], an exponential improvement. This leaves open the question of what happens for graphs of sublogarithmic width. To answer this, we...
...of polynomial size, the latter being, by Barrington s Theorem [1] the bigger class NC . On the other hand, Vinay [7] and Barrington et al. [2, 3] showed that by putting a geometric restriction on the computation, the di#erence disappears: The class of functions computable by...
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BibTeX entry: (Update)
D. M. Barrington, Ch-J Lu, P. B. Miltersen, S. Skyum, Searching constant width mazes captures the AC 0 Hierarchy. In Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science, 1998. http://citeseer.ist.psu.edu/barrington98searching.html More
@inproceedings{ barrington98searching,
author = "David A. Mix Barrington and Chi-Jen Lu and Peter Bro Miltersen and Sven Skyum",
title = "Searching Constant Width Mazes Captures the {AC} 0 Hierarchy",
booktitle = "Symposium on Theoretical Aspects of Computer Science",
pages = "73-83",
year = "1998",
url = "citeseer.ist.psu.edu/barrington98searching.html" }
Citations (may not include all citations):211 Languages that capture complexity classes - Immerman - 1987
63 Varieties of Formal Languages (context) - Pin - 1986
62 Lower Bounds for deterministic and nondeterministic branchin.. - Razborov - 1991
56 Finite monoids and the fine structure of NC (context) - Barrington, Th'erien - 1988
55 Hamilton paths in grid graphs (context) - Itai, Papadimitriou et al. - 1982
55 Classifying regular events in symbolic logic (context) - Thomas - 1982
50 Maintenance of a minimum spanning forest in a dynamic planar.. - Eppstein, Italiano et al. - 1992
48 Borel sets and circuit complexity (context) - Sipser - 1983
48 A complexity theory based on Boolean algebra (context) - Skyum, Valiant - 1985
38 The complexity of iterated multiplication - Immerman, Landau - 1995
20 Department of Information and Computer Science (context) - Eppstein, in et al. - 1996
13 Dynamic word problems - Frandsen, Miltersen et al. - 1997
6 On searching sorted lists: A near-optimal lower bound - Beame, Fich - 1997
3 or why mazes are easier to search than graphs (context) - Blum, Kozen et al. - 1978
2 On uniformity within NC 1 Journal of Computer and System Sci.. (context) - Barrington, Immerman et al.
2 Hardness of dynamic computation (context) - Husfeldt, Rauhe - 1997
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