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LoopClosing and Planarity in Topological MapBuilding
 In IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems (IROS
, 2004
"... Loopclosing has long been recognized as a critical issue when building maps of largescale environments from local observations. Topological mapping methods abstract the problem of determining the topological structure of the environment (i.e., how loops are closed) from the problem of determining ..."
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Cited by 19 (3 self)
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Loopclosing has long been recognized as a critical issue when building maps of largescale environments from local observations. Topological mapping methods abstract the problem of determining the topological structure of the environment (i.e., how loops are closed) from the problem of determining the metrical layout of places in the map and dealing with noisy sensors. A recently developed incremental topological mapping algorithm [1], [2] generates all possible topological maps consistent with the experienced sequence of actions and observations and the topological axioms. These are then ordered by a preference criterion such as minimality or probability, to determine the single best map for continued planning and exploration. This paper presents the planarity constraint and analyzes its impact on the searchtree of all topological maps consistent with (nonmetrical) exploration experience. Experimental studies demonstrate excellent results even in artificial environments where loopclosing is particularly difficult due to large amounts of perceptual aliasing and structural symmetry.
New Lower Bound Techniques For Dynamic Partial Sums and Related Problems
 SIAM Journal on Computing
, 2003
"... We study the complexity of the dynamic partial sum problem in the cellprobe model. We give the model access to nondeterministic queries and prove that the problem remains hard. We give the model access to the right answer as an oracle and prove that the problem remains hard. This suggests which kin ..."
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Cited by 8 (1 self)
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We study the complexity of the dynamic partial sum problem in the cellprobe model. We give the model access to nondeterministic queries and prove that the problem remains hard. We give the model access to the right answer as an oracle and prove that the problem remains hard. This suggests which kind of information is hard to maintain. From these results, we derive a number of lower bounds for dynamic algorithms and data structures: We prove lower bounds for dynamic algorithms for existential range queries, reachability in directed graphs, planarity testing, planar point location, incremental parsing, and fundamental data structure problems like maintaining the majority of the prefixes of a string of bits. We prove a lower bound for reachability in grid graphs in terms of the graph's width. We characterize the complexity of maintaining the value of any symmetric function on the prefixes of a bit string. Keywords. cellprobe model, partial sum, dynamic algorithm, data structure AMS subject classifications. 68Q17, 68Q10, 68Q05, 68P05
Hardness Results for Dynamic Problems by Extensions of Fredman and Saks' Chronogram Method
 In Proc. 25th Int. Coll. Automata, Languages, and Programming, number 1443 in Lecture Notes in Computer Science
, 1998
"... We introduce new models for dynamic computation based on the cell probe model of Fredman and Yao. We give these models access to nondeterministic queries or the right answer ±1 as an oracle. We prove that for the dynamic partial sum problem, these new powers do not help, the problem retains i ..."
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Cited by 8 (3 self)
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We introduce new models for dynamic computation based on the cell probe model of Fredman and Yao. We give these models access to nondeterministic queries or the right answer ±1 as an oracle. We prove that for the dynamic partial sum problem, these new powers do not help, the problem retains its lower bound of Omega (log n/ log log n). From...
Data Structures for TwoEdge Connectivity in Planar Graphs
 Comput. Sci
, 1994
"... We present a data structure for maintaining 2edge connectivity information dynamically in an embedded planar graph. The data structure requires linear storage and preprocessing time for its construction, supports online updates (deletion of an edge or insertion of an edge consistent with the embedd ..."
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Cited by 3 (0 self)
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We present a data structure for maintaining 2edge connectivity information dynamically in an embedded planar graph. The data structure requires linear storage and preprocessing time for its construction, supports online updates (deletion of an edge or insertion of an edge consistent with the embedding) in O(log 2 n) time, and answers a query (whether two vertices are in the same 2edgeconnected component) in O(log n) time. The previous best algorithm for this problem requires O(log 3 n) time for updates. 1 Introduction Connectivity in graphs is an important class of problems that has received considerable attention since the early work of Hopcroft and Tarjan, who designed lineartime algorithms for computing bi and triconnected components of a graph [1, 12, 17]. NC algorithms for 2 and 3connectivity have been proposed in [14, 18]. In recent years, attention has turned toward dynamic algorithms for graph connectivity. These algorithms maintain connectivity information as the...
Dynamic 2Connectivity With Backtracking
, 1998
"... . We give algorithms and data structures that maintain the 2edge and 2vertexconnected components of a graph under insertions and deletions of edges and vertices, where deletions occur in a backtracking fashion (i.e., deletions undo the insertions in the reverse order). Our algorithms ru ..."
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.<F3.83e+05> We give algorithms and data structures that maintain the 2edge and 2vertexconnected components of a graph under insertions and deletions of edges and vertices, where deletions occur in a backtracking fashion (i.e., deletions undo the insertions in the reverse order). Our algorithms run in #(log<F3.054e+05><F3.83e+05> n) worstcase time per operation and use<F3.054e+05><F3.83e+05> #(n) space, where<F3.054e+05> n<F3.83e+05> is the number of vertices. Using our data structure we can answer queries, which ask whether vertices<F3.054e+05> u<F3.83e+05> and<F3.054e+05> v<F3.83e+05> belong to the same 2connected component, in #(log<F3.054e+05><F3.83e+05> n) worstcase time.<F4.005e+05> Key words.<F3.83e+05> dynamic graph algorithms, backtracking<F4.005e+05> AMS subject classifications.<F3.83e+05> 68Q20, 68Q25<F4.005e+05> PII.<F3.83e+05> S0097539794272582<F5.251e+05> 1. Introduction.<F4.483e+05> Dynamic graph problems have been studied extensively in the last several years. Rou...
Incremental Convex Planarity Testing
, 2001
"... An important class of planar straightline drawings of graphs are convex drawings, in which all the faces are drawn as convex polygons. A planar graph is said to be convex planar if it admits a convex drawing. We give a new combinatorial characterization of convex planar graphs based on the decompos ..."
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An important class of planar straightline drawings of graphs are convex drawings, in which all the faces are drawn as convex polygons. A planar graph is said to be convex planar if it admits a convex drawing. We give a new combinatorial characterization of convex planar graphs based on the decomposition of a biconnected graph into its triconnected components. We then consider the problem of testing convex planarity in an incremental environment, where a biconnected planar graph is subject to online insertions of vertices and edges. We present a data structure for the online incremental convex planarity testing problem with the following performance, where n denotes the current number of vertices of the graph: (strictly) convex planarity testing takes O(1) worstcase time, insertion of vertices takes O(log n) worstcase time, insertion of edges takes O(log n) amortized time, and the space requirement of the data structure is O(n).