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27
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 520 (40 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.
Dynamic Graph Algorithms
, 1999
"... Introduction In many applications of graph algorithms, including communication networks, graphics, assembly planning, and VLSI design, graphs are subject to discrete changes, such as additions or deletions of edges or vertices. In the last decade there has been a growing interest in such dynamicall ..."
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Cited by 55 (0 self)
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Introduction In many applications of graph algorithms, including communication networks, graphics, assembly planning, and VLSI design, graphs are subject to discrete changes, such as additions or deletions of edges or vertices. In the last decade there has been a growing interest in such dynamically changing graphs, and a whole body of algorithms and data structures for dynamic graphs has been discovered. This chapter is intended as an overview of this field. In a typical dynamic graph problem one would like to answer queries on graphs that are undergoing a sequence of updates, for instance, insertions and deletions of edges and vertices. The goal of a dynamic graph algorithm is to update efficiently the solution of a problem after dynamic changes, rather than having to recompute it from scratch each time. Given their powerful versatility, it is not surprising that dynamic algorithms and dynamic data structures are often more difficult to design and analyze than their static c
Efficiently Solving Dynamic Markov Random Fields using Graph Cuts
 in: IEEE International Conference on Computer Vision (ICCV
, 2005
"... In this paper we present a fast new fully dynamic algorithm for the stmincut/maxflow problem. We show how this algorithm can be used to efficiently compute MAP estimates for dynamically changing MRF models of labelling problems in computer vision, such as image segmentation. Specifically, given th ..."
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Cited by 53 (9 self)
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In this paper we present a fast new fully dynamic algorithm for the stmincut/maxflow problem. We show how this algorithm can be used to efficiently compute MAP estimates for dynamically changing MRF models of labelling problems in computer vision, such as image segmentation. Specifically, given the solution of the maxflow problem on a graph, we show how to efficiently compute the maximum flow in a modified version of the graph. Our experiments showed that the time taken by our algorithm is roughly proportional to the number of edges whose weights were different in the two graphs. We test the performance of our algorithm on one particular problem: the objectbackground segmentation problem for video and compare it with the best known stmincut algorithm. The results show that the dynamic graph cut algorithm is much faster than its static counterpart and enables real time image segmentation. It should be noted that our method is generic and can be used to yield similar improvements in many other cases that involve dynamic change in the graph. 1.
DynFO: A Parallel, Dynamic Complexity Class
 Journal of Computer and System Sciences
, 1994
"... Traditionally, computational complexity has considered only static problems. Classical Complexity Classes such as NC, P, and NP are defined in terms of the complexity of checking  upon presentation of an entire input  whether the input satisfies a certain property. For many applications of compu ..."
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Cited by 50 (4 self)
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Traditionally, computational complexity has considered only static problems. Classical Complexity Classes such as NC, P, and NP are defined in terms of the complexity of checking  upon presentation of an entire input  whether the input satisfies a certain property. For many applications of computers it is more appropriate to model the process as a dynamic one. There is a fairly large object being worked on over a period of time. The object is repeatedly modified by users and computations are performed. We develop a theory of Dynamic Complexity. We study the new complexity class, Dynamic FirstOrder Logic (DynFO). This is the set of properties that can be maintained and queried in firstorder logic, i.e. relational calculus, on a relational database. We show that many interesting properties are in DynFO including multiplication, graph connectivity, bipartiteness, and the computation of minimum spanning trees. Note that none of these problems is in static FO, and this f...
Dynamic Graph Cuts for Efficient Inference in Markov Random Fields
"... In this paper we present a fast new fully dynamic algorithm for the stmincut/maxflow problem. We show how this algorithm can be used to efficiently compute MAP solutions for certain dynamically changing MRF models in computer vision such as image segmentation. Specifically, given the solution of ..."
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Cited by 47 (2 self)
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In this paper we present a fast new fully dynamic algorithm for the stmincut/maxflow problem. We show how this algorithm can be used to efficiently compute MAP solutions for certain dynamically changing MRF models in computer vision such as image segmentation. Specifically, given the solution of the maxflow problem on a graph, the dynamic algorithm efficiently computes the maximum flow in a modified version of the graph. The time taken by it is roughly proportional to the total amount of change in the edge weights of the graph. Our experiments show that, when the number of changes in the graph is small, the dynamic algorithm is significantly faster than the best known static graph cut algorithm. We test the performance of our algorithm on one particular problem: the objectbackground segmentation problem for video. It should be noted that the application of our algorithm is not limited to the above problem, the algorithm is generic and can be used to yield similar improvements in many other cases that involve dynamic change.
Dynamizing static algorithms with applications to dynamic trees and history independence
 In ACMSIAM Symposium on Discrete Algorithms (SODA
, 2004
"... We describe a machine model for automatically dynamizing static algorithms and apply it to historyindependent data structures. Static programs expressed in this model are dynamized automatically by keeping track of dependences between code and data in the form of a dynamic dependence graph. To study ..."
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Cited by 43 (26 self)
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We describe a machine model for automatically dynamizing static algorithms and apply it to historyindependent data structures. Static programs expressed in this model are dynamized automatically by keeping track of dependences between code and data in the form of a dynamic dependence graph. To study the performance of such automatically dynamized algorithms we present an analysis technique based on trace stability. As an example of the use of the model, we dynamize the Parallel Tree Contraction Algorithm of Miller and Reif to obtain a historyindependent data structure for the dynamic trees problem of Sleator and Tarjan. 1
An experimental analysis of selfadjusting computation
 In Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI
, 2006
"... Selfadjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a r ..."
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Cited by 35 (19 self)
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Selfadjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a reasonably broad range of applications. In this article, we describe algorithms and implementation techniques to realize selfadjusting computation and present an experimental evaluation of the proposed approach on a variety of applications, ranging from simple list primitives to more sophisticated computational geometry algorithms. The results of the experiments show that the approach is effective in practice, often offering orders of magnitude speedup from recomputing the output from scratch. We believe this is the first experimental evidence that incremental computation of any type is effective in practice for a reasonably broad set of applications.
ONLINE PLANARITY TESTING
, 1996
"... The online planaritytesting problem consists of performing the following operations on a planar graph G: (i) testing if a new edge can be added to G so that the resulting graph is itself planar; (ii) adding vertices and edges such that planarity is preserved. An efficient technique for online plan ..."
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Cited by 26 (2 self)
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The online planaritytesting problem consists of performing the following operations on a planar graph G: (i) testing if a new edge can be added to G so that the resulting graph is itself planar; (ii) adding vertices and edges such that planarity is preserved. An efficient technique for online planarity testing of a graph is presented that uses O(n) space and supports tests and insertions of vertices and edges in O(log n) time, where n is the current number of vertices of G. The bounds for tests and vertex insertions are worstcase and the bound for edge insertions is amortized. We also present other applications of this technique to dynamic algorithms for planar graphs.
An Experimental Analysis of Change Propagation in Dynamic Trees
, 2005
"... Change propagation is a technique for automatically adjusting the output of an algorithm to changes in the input. The idea behind change propagation is to track the dependences between data and function calls, so that, when the input changes, functions affected by that change can be reexecuted to u ..."
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Cited by 21 (13 self)
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Change propagation is a technique for automatically adjusting the output of an algorithm to changes in the input. The idea behind change propagation is to track the dependences between data and function calls, so that, when the input changes, functions affected by that change can be reexecuted to update the computation and the output. Change propagation makes it possible for a compiler to dynamize static algorithms. The practical effectiveness of change propagation, however, is not known. In particular, the cost of dependence tracking and change propagation may seem significant. The contributions of the paper are twofold. First, we present some experimental evidence that change propagation performs well when compared to direct implementations of dynamic algorithms. We implement change propagation on treecontraction as a solution to the dynamic trees problem and present an experimental evaluation of the approach. As a second contribution, we present a library for dynamictrees that support a general interface and present an experimental evaluation by considering a broad set of applications. The dynamictrees library relies on change propagation to handle edge insertions/deletions. The applications that we consider include path queries, subtree queries, leastcommonancestor queries, maintenance of centers and medians of trees, nearestmarkedvertex queries, semidynamic minimum spanning trees, and the maxflow algorithm of Sleator and Tarjan.
Dynamic Word Problems
, 1993
"... Let M be a fixed finite monoid. We consider the problem of implementing a data type containing a vector x = (x1 ; x2 ; : : : ; xn) 2 M n , initially (1; 1; : : : ; 1), with two kinds of operations, for each i 2 f1; : : : ; ng and a 2 M , an operation change i;a which changes x i to a and a singl ..."
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Cited by 19 (6 self)
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Let M be a fixed finite monoid. We consider the problem of implementing a data type containing a vector x = (x1 ; x2 ; : : : ; xn) 2 M n , initially (1; 1; : : : ; 1), with two kinds of operations, for each i 2 f1; : : : ; ng and a 2 M , an operation change i;a which changes x i to a and a single operation product returning Q n i=1 x i . This is the dynamic word problem for M . If we in addition for each j 2 f1; : : : ; ng have an operation prefix j returning Q j i=1 x i , we get the dynamic prefix problem for M . We analyze the complexity of these problems in the cell probe or decision assignment tree model for two natural cell sizes, 1 bit and log n bits. We obtain a partial classification of the complexity based on algebraic properties of M .