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28
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 68 (26 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.
FirstOrder Incremental Evaluation of Datalog Queries
 Annals of Mathematics and Artificial Intelligence
, 1993
"... We consider the problem of repeatedly evaluating the same (computationally expensive) query to a database that is being updated between successive query requests. In this situation, it should be possible to use the difference between successive database states and the answer to the query in one stat ..."
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Cited by 50 (17 self)
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We consider the problem of repeatedly evaluating the same (computationally expensive) query to a database that is being updated between successive query requests. In this situation, it should be possible to use the difference between successive database states and the answer to the query in one state to reduce the cost of evaluating the query in the next state. We use firstorder queries to compute the differences, and call this process "firstorder incremental query evaluation." After formalizing the notion of firstorder incremental query evaluation, we give an algorithm that constructs, for each regular chain query (including transitive closure as a special case), a nonrecursive program to compute the difference between the answer after an update and the answer before the update. We then extend this result to weakly regular queries, which are regular chain programs augmented with conjunctive queries having the socalled cartesianclosed increment property, and to the case of unbound...
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
Maintenance Of Transitive Closures And Transitive Reductions Of Graphs
, 1987
"... this paper appeared in the Proceedings of the 13th lat. Workshop on "GraphTheoretic Concepts in Computer Science" (WG '87), June 29 July 1, 1987, Kloster Banz/Staffelstein (FIG), published as: Lecture Notes in Computer Science, Vol. 314, SpringerVerlag, Berlin, 1988, pp. 106  120 ..."
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Cited by 39 (0 self)
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this paper appeared in the Proceedings of the 13th lat. Workshop on "GraphTheoretic Concepts in Computer Science" (WG '87), June 29 July 1, 1987, Kloster Banz/Staffelstein (FIG), published as: Lecture Notes in Computer Science, Vol. 314, SpringerVerlag, Berlin, 1988, pp. 106  120
Parallel RealTime Optimization: Beyond Speedup
 PARALLEL PROCESSING LETTERS
, 1999
"... Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? ..."
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Cited by 27 (25 self)
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Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for realtime optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the bestpossible approximation to the minimumweight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimumweight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained seque...
Nonrecursive Incremental Evaluation of Datalog Queries
 Annals of Mathematics and Artificial Intelligence
, 1995
"... We consider the problem of repeatedly evaluating the same (computationally expensive) query to a database that is being updated between successive query requests. In this situation, it should be possible to use the difference between successive database states and the answer to the query in one stat ..."
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Cited by 21 (8 self)
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We consider the problem of repeatedly evaluating the same (computationally expensive) query to a database that is being updated between successive query requests. In this situation, it should be possible to use the difference between successive database states and the answer to the query in one state to reduce the cost of evaluating the query in the next state. We use nonrecursive Datalog (which are unions of conjunctive queries) to compute the differences, and call this process "incremental query evaluation using conjunctive queries." After formalizing the notion of incremental query evaluation using conjunctive queries, we give an algorithm that constructs, for each regular chain query (including transitive closure as a special case), a nonrecursive Datalog program to compute the difference between the answer after an update and the answer before the update. We then extend this result to weakly regular queries, which are regular chain programs augmented with conjunctive queries havin...
Parallel RealTime Numerical Computation: Beyond Speedup III
 International Journal of Computers and their Applications, Special Issue on High Performance Computing Systems
"... Parallel computers can do more than simply speed up sequential computations. They are capable of finding solutions that are far better in quality than those obtained by sequential computers. This fact is demonstrated by analyzing sequential and parallel solutions to numerical problems in a realtime ..."
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Cited by 16 (15 self)
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Parallel computers can do more than simply speed up sequential computations. They are capable of finding solutions that are far better in quality than those obtained by sequential computers. This fact is demonstrated by analyzing sequential and parallel solutions to numerical problems in a realtime paradigm. In this setting, numerical data required to solve a problem are received as input by a computer system, at regular intervals. The computer must process its inputs as soon as they arrive. It must also produce its outputs at regular intervals, as soon as they are available. We show that for some realtime numerical problems a parallel computer can deliver a solution that is significantly more accurate than when computed by a sequential computer. Similar results were derived recently in the areas of realtime optimization and realtime cryptography. Key words and phrases: Parallelism, realtime computation, numerical analysis. This research was supported by the Natural Sciences a...
Parallel RealTime Computation: Sometimes Quantity Means Quality
 Computing and Informatics
, 2000
"... The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. As a consequence, interest in parallel computation to date has naturally focused on the speedup provided by parallel algorithms over their sequential counterparts. Th ..."
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Cited by 15 (14 self)
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The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. As a consequence, interest in parallel computation to date has naturally focused on the speedup provided by parallel algorithms over their sequential counterparts. The thesis of this paper is that a second equally important motivation for using parallel computers exists. Specifically, the following question is posed: Can parallel computers, thanks to their multiple processors, do more than simply speed up the solution to a problem? We show that within the paradigm of realtime computation, some classes of problems have the property that a solution to a problem in the class, when computed in parallel, is far superior in quality than the best one obtained on a sequential computer. What constitutes a better solution depends on the problem under consideration. Thus, `better' means `closer to optimal' for optimization problems, `more secure' for crypto...
Incremental Maintenance of Recursive Views Using Relational Calculus/SQL
 SIGMOD Record
, 2000
"... Views are a central component of both traditional database systems and new applications such as data warehouses. Very often the desired views (e.g. the transitive closure) cannot be defined in the standard language of the underlying database system. Fortunately, it is often possible to incrementall ..."
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Cited by 15 (1 self)
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Views are a central component of both traditional database systems and new applications such as data warehouses. Very often the desired views (e.g. the transitive closure) cannot be defined in the standard language of the underlying database system. Fortunately, it is often possible to incrementally maintain these views using the standard language. For example, transitive closure of acyclic graphs, and of undirected graphs, can be maintained in relational calculus after both single edge insertions and deletions. Many such results have been published in the theoretical database community. The purpose of this survey is to make these useful results known to the wider database research and development community. There are many interesting issues involved in the maintenance of recursive views. A maintenance algorithm may be applicable to just one view, or to a class of views specified by a view definition language such as Datalog. The maintenance algorithm can be specified in a maintenance language of different expressiveness, such as the conjunctive queries, the relational calculus or SQL. Ideally, this maintenance language should be less expensive than the view definition language. The maintenance algorithm may allow updates of different kinds, such as just single tuple insertions, just single tuple deletions, special setbased insertions and/or deletions, or combinations thereof. The view maintenance algorithms may also need to maintain auxiliary relations to help maintain the views of interest. It is of interest to know the minimal arity necessary for these auxiliary relations