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Trading Space for Time in Undirected st Connectivity
 In Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing
, 1991
"... Aleliunas et al. [1] posed the following question: "The reachability problem for undirected graphs can be solved in logspace and O.mn/ time [m is the number of edges and n is the number of vertices] by a probabilistic algorithm that simulates a random walk, or in linear time and space by a conven ..."
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Cited by 22 (3 self)
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Aleliunas et al. [1] posed the following question: "The reachability problem for undirected graphs can be solved in logspace and O.mn/ time [m is the number of edges and n is the number of vertices] by a probabilistic algorithm that simulates a random walk, or in linear time and space by a conventional deterministic graph traversal algorithm. Is there a spectrum of timespace tradeoffs between these extremes?" We answer this question in the affirmative for graphs with a linear number of edges by presenting an algorithm that is faster than the random walk by a factor essentially proportional to the size of its workspace. For denser graphs, our algorithm is faster than the random walk but the speedup factor is smaller. v 1 Motivation and Results We consider the problem of st connectivity on an undirected graph (USTCON). Given a graph G with n vertices and m edges, and given two vertices s and t of G, we are to decide if s and t are in the same connected component. We are in...
Reachability and the Power of Local Ordering
, 1994
"... The L ? = NL question remains one of the major unresolved problems in complexity theory. Both L and NL have logical characterizations as the sets of totally ordered () structures expressible in firstorder logic augmented with the appropriate Transitive Closure operator [I87]: (FO+DTC+ ) captur ..."
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Cited by 16 (4 self)
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The L ? = NL question remains one of the major unresolved problems in complexity theory. Both L and NL have logical characterizations as the sets of totally ordered () structures expressible in firstorder logic augmented with the appropriate Transitive Closure operator [I87]: (FO+DTC+ ) captures L and (FO+TC+ ) captures NL. On the other hand, in the absence of ordering, (FO + TC) is strictly more powerful than (FO +DTC) [GM92]. An apparently quite different "structured" model of logspace machines is the Jumping Automaton on Graphs (JAG), [CR80]. We show that the JAG model is intimately related to these logics on "oneway locally ordered" (1LO) structures. We argue that the usual JAG model is unreasonably weak and should be replaced, wherever possible, by the twoway JAG model, which we define. Furthermore, the language (FO + DTC + 2LO) over twoway locally ordered (2LO) graphs is more robust than even the twoway JAG model, and yet lower bounds remain accessible. We pro...
A Spectrum of TimeSpace Tradeoffs for Undirected st Connectivity
, 1996
"... We present a family of randomized algorithms that enjoys a wide range of timespace tradeoffs in deciding undirected STconnectivity. Our tradeoffs cover the whole range between Breadth First Search and the random walk procedure of Aleliunas et al., and achieve a timespace product of ~ O(mn) (wher ..."
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Cited by 9 (0 self)
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We present a family of randomized algorithms that enjoys a wide range of timespace tradeoffs in deciding undirected STconnectivity. Our tradeoffs cover the whole range between Breadth First Search and the random walk procedure of Aleliunas et al., and achieve a timespace product of ~ O(mn) (where n is the number of vertices in the graph, m is the number of edges, and ~ O notation is used in order to suppress logarithmic terms). Moreover, we obtain improved timespace tradeoffs of ~ O(n 2) for regular graphs. A convenient and informative way of expressing our tradeoffs, that implies the tradeoffs stated above, is as ~ O(( P n i=1 d i)( P n i=1 1=d i)), where d i is the degree of vertex i in the input graph. In constructing our algorithms and analysing them, we build upon earlier work of Broder et al. (who achieved a timespace tradeoff of ~ O(m 2
Automata with nested pebbles capture firstorder logic with transitive closure
 Logical Methods in Computer Science
"... Vol. 3 (2:3) 2007, pp. 1–27 ..."
Automated ImageBased Mapping
, 1998
"... We describe an approach to the automated construction of visual maps of an unknown environment. These maps take the form of imagebased "walkthroughs" rather than 2D or 3D models. Our approach is based on the selection of informative viewpoints within the environment. These viewpoints are locations ..."
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Cited by 6 (5 self)
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We describe an approach to the automated construction of visual maps of an unknown environment. These maps take the form of imagebased "walkthroughs" rather than 2D or 3D models. Our approach is based on the selection of informative viewpoints within the environment. These viewpoints are locations in the environment associated with views containing maximal visual interest. This approach to environment representation is analogous to image compression. Our goal is to obtain a set of representative views resembling those that would be selected by a human observer given the same task. Our computational procedure is inspired by models of human visual attention appearing in the literature on human psychophysics. We make use of the underlying edge structure of a scene, as it is largely una #ected by variations in illumination. Our implementation uses a mobile robot to traverse the environment, and then builds an imagebased virtual representation of the environment, only keeping the views whose responses were highest. We demonstrate the e#ectiveness of our attention operator on both single images, and in viewpoint selection within an unknown environment. Keywords: imagebased virtual reality, environment representation, visual attention, mobile robotics I.
Traversal of a QuasiPlanar Subdivision without Using Mark Bits (Extended Abstract)
 4th International Workshop on Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks (WMAN’04), Fanta Fe
, 2004
"... E. Chvez Escuela de Ciencias FsicoMatemticas Universidad Michoacana, Mxico S. Dobrev # School of IT and Engineering University of Ottawa, Canada E. Kranakis + School of Computer Science Carleton University, Canada J. Opatrn # Department of Computer Science Concordia University, Canada L ..."
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Cited by 5 (5 self)
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E. Chvez Escuela de Ciencias FsicoMatemticas Universidad Michoacana, Mxico S. Dobrev # School of IT and Engineering University of Ottawa, Canada E. Kranakis + School of Computer Science Carleton University, Canada J. Opatrn # Department of Computer Science Concordia University, Canada L. Stacho Department of Mathematics Simon Fraser University, Canada J. Urrutia Instituto de Matemticas Universidad Nacional Autnoma de Mxico Mxico Abstract The problem of traversal of planar subdivisions or other graphlike structures without using mark bits is central to many realworld applications [7, 8, 11, 13, 12, 17, 18]. First such algorithms developed were able to traverse triangulated subdivisions [10]. Later these algorithm were extended to traverse vertices of an arrangement or a convex polytope [3]. The research progress culminated to an algorithm that can traverse any planar subdivision [6, 9]. In this paper, we extend the notion of planar subdivision to quasiplanar subdivision in which we allow many edges to cross each other. We generalize the algorithm from [9] to traverse any quasiplanar subdivision that satisfies a simple requirement. If we use techniques from [6] the worst case running time of our algorithm will be O(E log E); which matches with the running time of the traversal algorithm for planar subdivisions [6].
Viewpoint Selection  An Autonomous Robotic System for Virtual Environment Creation
 in Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems
, 1998
"... This paper describes an integrated system for the automatic construction of imagebased virtual realities to describe a real environment. A mobile robot autonomously navigates through the environment and uses a camera to make observations. At locations that are deemed su#ciently interesting, panoram ..."
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Cited by 3 (1 self)
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This paper describes an integrated system for the automatic construction of imagebased virtual realities to describe a real environment. A mobile robot autonomously navigates through the environment and uses a camera to make observations. At locations that are deemed su#ciently interesting, panoramic images are collected that are used to construct a multinode VR movie. Images of the environment are classified in terms of two features related to human attention: edge element density and edge orientation. The system deems locations interesting if they are su#ciently di#erent from the surrounding environment. The parameterization of the surrounding environment is computed either in a precomputation pass, or online using a technique termed alphabacktracking. The panoramic images that describe the environment are automatically joined together in a navigable movie that simulates motion in the real environment. 1