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17
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar graphs. These algorithms adopt a variety of representations (e.g., straightline, polyline, visibility), and update the drawing in a smooth way.
Cell probe complexity  a survey
 In 19th Conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 1999. Advances in Data Structures Workshop
"... The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1 ..."
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Cited by 33 (0 self)
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The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1
Parallel transitive closure and point location in planar structures
 SIAM J. COMPUT
, 1991
"... Parallel algorithms for several graph and geometric problems are presented, including transitive closure and topological sorting in planar stgraphs, preprocessing planar subdivisions for point location queries, and construction of visibility representations and drawings of planar graphs. Most of th ..."
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Cited by 22 (10 self)
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Parallel algorithms for several graph and geometric problems are presented, including transitive closure and topological sorting in planar stgraphs, preprocessing planar subdivisions for point location queries, and construction of visibility representations and drawings of planar graphs. Most of these algorithms achieve optimal O(log n) running time using n = log n processors in the EREW PRAM model, n being the number of vertices.
Lower Bounds for Dynamic Transitive Closure, Planar Point Location, and Parentheses Matching
 Nordic Journal of Computing
, 1996
"... We give a number of new lower bounds in the cell probe model with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations. ..."
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Cited by 13 (4 self)
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We give a number of new lower bounds in the cell probe model with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations.
Dynamic Expression Trees
, 1991
"... We present a technique for dynamically maintaining a collection of arithmetic expressions represented by binary trees (whose leaves are variables and whose internal nodes are operators). A query operation asks for the value of an expression (associated with the root of a tree). Update operations inc ..."
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Cited by 11 (3 self)
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We present a technique for dynamically maintaining a collection of arithmetic expressions represented by binary trees (whose leaves are variables and whose internal nodes are operators). A query operation asks for the value of an expression (associated with the root of a tree). Update operations include changing the value of a variable and combining or decomposing expressions by linking or cutting the corresponding trees. Our dynamic data structure uses linear space and supports queries and updates in logarithmic time. An important application is the dynamic maintenance of maximum flow and shortest path in seriesparallel digraphs under a sequence of vertex and edge insertions, series and parallel compositions, and their respective inverses. Queries include reporting the maximum flow or shortest stpath in a seriesparallel subgraph.
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 11 (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 retai ..."
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Cited by 9 (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 &plusmn;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...
Fully Dynamic Planarity Testing in Planar Embedded Graphs
, 1993
"... We present the first data structure to maintain an embedded planar graph under arbitrary edge insertions, arbitrary edge deletions and queries that test whether the insertion of a new edge would violate the planarity of the embedding. Our data structure supports online updates and queries on an nv ..."
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Cited by 8 (1 self)
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We present the first data structure to maintain an embedded planar graph under arbitrary edge insertions, arbitrary edge deletions and queries that test whether the insertion of a new edge would violate the planarity of the embedding. Our data structure supports online updates and queries on an nvertex embedded planar graph in O(log 2 n) worstcase time, it can be built in O(n) time and requires O(n) space. This work was supported in part by ESPRIT BRA ALCOM II under contract no. 7141 and by the Italian MURST Project "Algoritmi, Modelli di Calcolo e Strutture Informative". A preliminary version of this paper was presented at the 1st European Symposium on Algorithms, Bad Honnef, Bonn, Germany [10]. y Dipartimento di Informatica e Sistemistica, Universit`a di Roma "La Sapienza", Roma, Italy. On leave from IBM T.J. Watson Research Center. z Department of Computer Science, Princeton University, Princeton, NJ 08544, USA. The research of this author was supported by a NATO Scienc...
Fully Dynamic Planarity Testing with Applications
"... The fully dynamic planarity testing problem consists of performing an arbitrary sequence of the following three kinds of operations on a planar graph G: (i) insert an edge if the resultant graph remains planar; (ii) delete an edge; and (iii) test whether an edge could be added to the graph without ..."
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Cited by 7 (0 self)
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The fully dynamic planarity testing problem consists of performing an arbitrary sequence of the following three kinds of operations on a planar graph G: (i) insert an edge if the resultant graph remains planar; (ii) delete an edge; and (iii) test whether an edge could be added to the graph without violating planarity. We show how to support each of the above operations in O(n2=3) time, where n is the number of vertices in the graph. The bound for tests and deletions is worstcase, while the bound for insertions is amortized. This is the first algorithm for this problem with sublinear running time, and it affirmatively answers a question posed in [11]. The same data structure has further applications in maintaining the biconnected and triconnected components of a dynamic planar graph. The time bounds are the same: O(n2=3) worstcase time per edge deletion, O(n2=3) amortized time per edge insertion, and O(n2=3) worstcase time to check whether two vertices are either biconnected or triconnected.
An externalmemory data structure for shortest path queries
 DIPLOMARBEIT, FRIEDRICHSCHILLERUNIVERSITIT JENA, NOV,1998
, 1998
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