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24
Polylogarithmic deterministic fullydynamic graph algorithms I: connectivity and minimum spanning tree
 JOURNAL OF THE ACM
, 1997
"... Deterministic fully dynamic graph algorithms are presented for connectivity and minimum spanning forest. For connectivity, starting with no edges, the amortized cost for maintaining a spanning forest is O(log² n) per update, i.e. per edge insertion or deletion. Deciding connectivity between any two ..."
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Cited by 125 (6 self)
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Deterministic fully dynamic graph algorithms are presented for connectivity and minimum spanning forest. For connectivity, starting with no edges, the amortized cost for maintaining a spanning forest is O(log² n) per update, i.e. per edge insertion or deletion. Deciding connectivity between any two given vertices is done in O(log n= log log n) time. This matches the previous best randomized bounds. The previous best deterministic bound was O( 3 p n log n) amortized time per update but constant time for connectivity queries. For minimum spanning trees, first a deletionsonly algorithm is presented supporting deletes in amortized time O(log² n). Applying a general reduction from Henzinger and King, we then get a fully dynamic algorithm such that starting with no edges, the amortized cost for maintaining a minimum spanning forest is O(log^4 n) per update. The previous best deterministic bound was O( 3 p n log n) amortized time per update, and no better randomized bounds were ...
Fully Dynamic All Pairs Shortest Paths with Real Edge Weights
 In IEEE Symposium on Foundations of Computer Science
, 2001
"... We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with realvalued edge weights. Given a dynamic directed graph G such that each edge can assume at most S di#erent real values, we show how to support updates in O(n amortized time and que ..."
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Cited by 35 (10 self)
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We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with realvalued edge weights. Given a dynamic directed graph G such that each edge can assume at most S di#erent real values, we show how to support updates in O(n amortized time and queries in optimal worstcase time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with onesided error which supports updates faster in O(S We also show how to obtain query/update tradeo#s for this problem, by introducing two new families of algorithms. Algorithms in the first family achieve an update bound of O(n/k), and improve over the best known update bounds for k in the . Algorithms in the second family achieve an update bound of ), and are competitive with the best known update bounds (first family included) for k in the range (n/S) # Work partially supported by the IST Programme of the EU under contract n. IST199914. 186 (ALCOMFT) and by CNR, the Italian National Research Council, under contract n. 01.00690.CT26. Portions of this work have been presented at the 42nd Annual Symp. on Foundations of Computer Science (FOCS 2001) [8] and at the 29th International Colloquium on Automata, Languages, and Programming (ICALP'02) [9].
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.
Parametric and Kinetic Minimum Spanning Trees
"... We consider the parametric minimum spanning treeproblem, in which we are given a graph with edge weights that are linear functions of a parameter * and wish tocompute the sequence of minimum spanning trees generated as * varies. We also consider the kinetic minimumspanning tree problem, in which * r ..."
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Cited by 30 (7 self)
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We consider the parametric minimum spanning treeproblem, in which we are given a graph with edge weights that are linear functions of a parameter * and wish tocompute the sequence of minimum spanning trees generated as * varies. We also consider the kinetic minimumspanning tree problem, in which * represents time and the graph is subject in addition to changes such as edge insertions, deletions, and modifications of the weight functions as time progresses. We solve both problems in time O(n2=3 log4=3 n) per combinatorial change in the tree (or randomized O(n2=3 log n) per change). Our time bounds reduce to O(n1=2 log3=2 n) per change (O(n1=2 log n) randomized) for planar graphs or other minorclosed families of graphs, and O(n1=4 log3=2 n) per change (O(n1=4 log n) randomized) for planar graphs with weight changes but no insertions or deletions.
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 29 (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
Kinetic Connectivity of Rectangles
 In Proc. 15th Annu. ACM Sympos. Comput. Geom
, 1999
"... We develop a kinetic data structure (KDS) for maintaining the connectivity of a set of axisaligned rectangles moving in the plane. In the kinetic framework, each rectangle is assumed to travel along a lowdegree algebraic path, specified by a flight planif the flight plan changes, the data struc ..."
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Cited by 16 (1 self)
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We develop a kinetic data structure (KDS) for maintaining the connectivity of a set of axisaligned rectangles moving in the plane. In the kinetic framework, each rectangle is assumed to travel along a lowdegree algebraic path, specified by a flight planif the flight plan changes, the data structure is informed about it. The connectivity of rectangles changes only at discrete moments, given by the times when the order of rectangles along either axis changes. Our main result is a kinetic data structure of size O(n log n) that requires O(log 2 n) amortized time for each update, and answers connectivity queries in worstcase time O(log n= log log n). 1 Introduction Connectivity is the most basic of graph properties, with many applications to realworld problems. Applications of connectivity range from electrical connectivity in integrated circuits to network connectivity in communication networks. In this paper, we explore the problem of maintaining the connectivity of n axisalig...
Paschos. Reoptimization of minimum and maximum traveling salesman’s tours
 J. Discrete Algorithms
"... Abstract. In this paper, reoptimization versions of the traveling salesman problem (TSP) are addressed. Assume that an optimum solution of an instance is given and the goal is to determine if one can maintain a good solution when the instance is subject to minor modifications. We study the case wher ..."
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Cited by 15 (2 self)
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Abstract. In this paper, reoptimization versions of the traveling salesman problem (TSP) are addressed. Assume that an optimum solution of an instance is given and the goal is to determine if one can maintain a good solution when the instance is subject to minor modifications. We study the case where nodes are inserted in, or deleted from, the graph. When inserting a node, we show that the reoptimization problem for MinTSP is approximable within ratio 4/3 if the distance matrix is metric. We show that, dealing with metric MaxTSP, a simple heuristic is asymptotically optimum when a constant number of nodes are inserted. In the general case, we propose a 4/5approximation algorithm for the reoptimization version of MaxTSP. 1
Implementation of Dynamic Trees with InSubtree Operations
 ACM Journal of Experimental Algorithms
, 1998
"... We describe an implementation of dynamic trees with \insubtree" operations. Our implementation follows Sleator and Tarjan's framework of dynamictree implementations based on splay trees. We consider the following two examples of \insubtree" operations. (a) For a given node v, nd a node with the m ..."
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Cited by 8 (0 self)
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We describe an implementation of dynamic trees with \insubtree" operations. Our implementation follows Sleator and Tarjan's framework of dynamictree implementations based on splay trees. We consider the following two examples of \insubtree" operations. (a) For a given node v, nd a node with the minimum key in the subtree rooted at v. (b) For a given node v, nd a random node with key X in the subtree rooted at v (value X is xed throughout the whole computation). The rst operation may provide support for edge deletions in the dynamic minimum spanning tree problem. The second one may be useful in local search methods for degreeconstrained minimum spanning tree problems. We conducted experiments with our dynamictree implementation within these two contexts, and the results suggest that this implementation may lead to considerably faster codes than straightforward approaches do. 1. INTRODUCTION A dynamic tree collection (or simply dynamic trees) is a data structure which maintain...
A SelfConfiguring Resolver Architecture for Resource Discovery and Routing in Device Networks
, 2000
"... Network environments of the future will be characterized by a variety of mobile and wireless devices in addition to generalpurpose computers. Such environments display a degree of dynamism not usually seen in traditional wired networks due to mobility of nodes and services, rapid uctuations in perf ..."
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Cited by 7 (0 self)
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Network environments of the future will be characterized by a variety of mobile and wireless devices in addition to generalpurpose computers. Such environments display a degree of dynamism not usually seen in traditional wired networks due to mobility of nodes and services, rapid uctuations in performance, and node failures. This combination of heterogeneity and dynamism makes it hard for applications to discover the network locations of services that best satisfy their needs. This thesis presents a communication system that allows network applications to send messages by describing the attributes of the intended destinations for their messages, rather than by explicitly listing the network locations (e.g., IP addresses) of the message destinations. Senders are thus relieved from having to know in priori the destination network locations, and receiver nodes are determined during message delivery time by the system, allowing them to be mobile, grouped, or dynamically adapted to differ...
Dynamically Switching Vertices in Planar Graphs
 ALGORITHMICA
, 2000
"... We consider graphs whose vertices may be in one of two different states: either on or off. We wish to maintain dynamically such graphs under an intermixed sequence of updates and queries. An update may reverse the status of a vertex, by switching it either on or off, and may insert a new edge or ..."
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Cited by 6 (0 self)
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We consider graphs whose vertices may be in one of two different states: either on or off. We wish to maintain dynamically such graphs under an intermixed sequence of updates and queries. An update may reverse the status of a vertex, by switching it either on or off, and may insert a new edge or delete an existing edge. A query tests whether any two given vertices are connected in the subgraph induced by the vertices that are on. We give efficient algorithms that maintain information about connectivity on planar graphs in O(log³ n) amortized time per query, insert, delete, switchon and switchoff operation over sequences of at least\Omega\Gamma n) operations, where n is the number of vertices of the graph.