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29
Maintenance of a Minimum Spanning Forest in a Dynamic Plane Graph
, 1992
"... We give an efficient algorithm for maintaining a minimum spanning forest of a plane graph subject to online modifications. The modifications supported include changes in the edge weights, and insertion and deletion of edges and vertices which are consistent with the given embedding. Our algorithm r ..."
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Cited by 64 (25 self)
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We give an efficient algorithm for maintaining a minimum spanning forest of a plane graph subject to online modifications. The modifications supported include changes in the edge weights, and insertion and deletion of edges and vertices which are consistent with the given embedding. Our algorithm runs in O(log n) time per operation and O(n) space.
Fully Dynamic Algorithms for Maintaining AllPairs Shortest Paths and Transitive Closure in Digraphs
 IN PROC. 40TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS’99
, 1999
"... This paper presents the first fully dynamic algorithms for maintaining allpairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2 + ffl), for any positive constant ffl, the amortized update time is O(n 2 log 2 n= log ..."
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Cited by 63 (0 self)
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This paper presents the first fully dynamic algorithms for maintaining allpairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2 + ffl), for any positive constant ffl, the amortized update time is O(n 2 log 2 n= log log n); for an error factor of (1 + ffl) the amortized update time is O(n 2 log 3 (bn)=ffl 2 ). For exact shortest paths the amortized update time is O(n 2:5 p b log n). Query time for exact and approximate shortest distances is O(1); exact and approximate paths can be generated in time proportional to their lengths. Also presented is a fully dynamic transitive closure algorithm with update time O(n 2 log n) and query time O(1). The previously known fully dynamic transitive closure algorithm with fast query time has onesided error and update time O(n 2:28 ). The algorithms use simple data structures, and are deterministic.
A Fully Dynamic Algorithm for Maintaining the Transitive Closure
 In Proc. 31st ACM Symposium on Theory of Computing (STOC'99
, 1999
"... This paper presents an efficient fully dynamic graph algorithm for maintaining the transitive closure of a directed graph. The algorithm updates the adjacency matrix of the transitive closure with each update to the graph. Hence, each reachability query of the form "Is there a directed path from i t ..."
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Cited by 43 (1 self)
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This paper presents an efficient fully dynamic graph algorithm for maintaining the transitive closure of a directed graph. The algorithm updates the adjacency matrix of the transitive closure with each update to the graph. Hence, each reachability query of the form "Is there a directed path from i to j?" can be answered in O(1) time. The algorithm is randomized; it is correct when answering yes, but has O(1/n^c) probability of error when answering no, for any constant c. In acyclic graphs, worst case update time is O(n^2). In general graphs, update time is O(n^(2+alpha)), where alpha = min {.26, maximum size of a strongly connected component}. The space complexity of the algorithm is O(n^2).
Fully Dynamic Transitive Closure: Breaking Through The O(n²) Barrier
 IN PROC. IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 2000
"... In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive closure. In particular, we devise a deterministic algorithm for g ..."
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Cited by 41 (7 self)
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In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive closure. In particular, we devise a deterministic algorithm for general directed graphs that achieves O(n²) amortized time for updates, while preserving unit worstcase cost for queries. In case of deletions only, our algorithm performs updates faster in O(n) amortized time. Our
Improved Dynamic Reachability Algorithms for Directed Graphs
, 2002
"... We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph, and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. Among our algorithms are: (i) A decremental algorithm for maintaining the ..."
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Cited by 29 (3 self)
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We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph, and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. Among our algorithms are: (i) A decremental algorithm for maintaining the transitive closure of a directed graph, through an arbitrary sequence of edge deletions, in O(mn) total expected time, essentially the time needed for computing the transitive closure of the initial graph. Such a result was previously known only for acyclic graphs.
Lifelong Planning A*
, 2005
"... Heuristic search methods promise to find shortest paths for pathplanning problems faster than uninformed search methods. Incremental search methods, on the other hand, promise to find shortest paths for series of similar pathplanning problems faster than is possible by solving each pathplanning p ..."
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Cited by 29 (3 self)
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Heuristic search methods promise to find shortest paths for pathplanning problems faster than uninformed search methods. Incremental search methods, on the other hand, promise to find shortest paths for series of similar pathplanning problems faster than is possible by solving each pathplanning problem from scratch. In this article, we develop Lifelong Planning A * (LPA*), an incremental version of A * that combines ideas from the artificial intelligence and the algorithms literature. It repeatedly finds shortest paths from a given start vertex to a given goal vertex while the edge costs of a graph change or vertices are added or deleted. Its first search is the same as that of a version of A * that breaks ties in favor of vertices with smaller gvalues but many of the subsequent searches are potentially faster because it reuses those parts of the previous search tree that are identical to the new one. We present analytical results that demonstrate its similarity to A * and experimental results that demonstrate its potential advantage in two different domains if the pathplanning problems change only slightly and the changes are close to the goal.
A fully dynamic reachability algorithm for directed graphs with an almost linear update time
 In Proc. of ACM Symposium on Theory of Computing
, 2004
"... We obtain a new fully dynamic algorithm for the reachability problem in directed graphs. Our algorithm has an amortized update time of O(m+n log n) and a worstcase query time of O(n), where m is the current number of edges in the graph, and n is the number of vertices in the graph. Each update oper ..."
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Cited by 27 (1 self)
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We obtain a new fully dynamic algorithm for the reachability problem in directed graphs. Our algorithm has an amortized update time of O(m+n log n) and a worstcase query time of O(n), where m is the current number of edges in the graph, and n is the number of vertices in the graph. Each update operation either inserts a set of edges that touch the same vertex, or deletes an arbitrary set of edges. The algorithm is deterministic and uses fairly simple data structures. This is the first algorithm that breaks the O(n 2) update barrier for all graphs with o(n 2)edges. One of the ingredients used by this new algorithm may be interesting in its own right. It is a new dynamic algorithm for strong connectivity in directed graphs with an interesting persistency property. Each insert operation creates a new version of the graph. A delete operation deletes edges from all versions. Strong connectivity queries can be made on each version of the graph. The algorithm handles each update in O(mα(m, n)) amortized time, and each query in O(1) time, where α(m, n) is a functional inverse of Ackermann’s function appearing in the analysis of the unionfind data structure. Note that the update time of O(mα(m, n)), in case of a delete operation, is the time needed for updating all versions of the graph. Categories and Subject Descriptors G.2.2 [Discrete Mathematics]: Graph Theory—Graph algorithms, Path and circuit problems
Integrity Constraint and Rule Maintenance in Temporal Deductive Knowledge Bases
, 1993
"... The enforcement of semantic integrity constraints in data and knowledge bases constitutea a major performance bottleneck. Integrity constraint simplification methods aim at reducing the complexity of formula evaluation at runtime. This paper proposes such a simplification method for large and seman ..."
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Cited by 22 (7 self)
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The enforcement of semantic integrity constraints in data and knowledge bases constitutea a major performance bottleneck. Integrity constraint simplification methods aim at reducing the complexity of formula evaluation at runtime. This paper proposes such a simplification method for large and semantically rich knowledge bases. Structural, temporal and assertional knowledge in the form of deductive rules and integrity constraints, is represented in Telos, a hybrid language for knowledge representation. A compilation method performs a number of syntactic, semantic and temporal transformations to integrity constraints and deductive rules, and organizes simplified forms in a dependence graph that allows for efficient computati.on of implicit updates. Precomputation of potential implicit updates at compile time is possible by computing the dependence graph transitive closure. To account for dynamic changes to the dependence graph by updates of constraints and rules, we propose efficient algorithms for the incremental maintenance of the computed transitive closure.
Fast replanning for navigation in unknown terrain
 Transactions on Robotics
"... Abstract—Mobile robots often operate in domains that are only incompletely known, for example, when they have to move from given start coordinates to given goal coordinates in unknown terrain. In this case, they need to be able to replan quickly as their knowledge of the terrain changes. Stentz ’ Fo ..."
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Cited by 22 (7 self)
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Abstract—Mobile robots often operate in domains that are only incompletely known, for example, when they have to move from given start coordinates to given goal coordinates in unknown terrain. In this case, they need to be able to replan quickly as their knowledge of the terrain changes. Stentz ’ Focussed Dynamic A (D) is a heuristic search method that repeatedly determines a shortest path from the current robot coordinates to the goal coordinates while the robot moves along the path. It is able to replan faster than planning from scratch since it modifies its previous search results locally. Consequently, it has been extensively used in mobile robotics. In this article, we introduce an alternative to D that determines the same paths and thus moves the robot in the same way but is algorithmically different. D Lite is simple, can be rigorously analyzed, extendible in multiple ways, and is at least as efficient as D. We believe that our results will make Dlike replanning methods even more popular and enable robotics researchers to adapt them to additional applications. Index Terms—A, D (Dynamic A), navigation in unknown terrain, planning with the freespace assumption, replanning, search, sensorbased path planning. I.
Online Graph Algorithms for Incremental Compilation
, 1992
"... Compilers usually construct various data structures which often vary only slightly fi'om compilation run to compilation run. This paper gives various solutions to the problems of quickly updating these data structures instead of building them from scratch each time. All problems we found can be redu ..."
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Cited by 19 (0 self)
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Compilers usually construct various data structures which often vary only slightly fi'om compilation run to compilation run. This paper gives various solutions to the problems of quickly updating these data structures instead of building them from scratch each time. All problems we found can be reduced to graph problems. Specifically, we give algorithms for updating data structures for the problems of topological order, loop detection, and reachability from the start routine.