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30
A.: Minimum spanning tree on spatiotemporal networks
 In: Proc. of the 21st Intl. Conf. on Database and expert systems applications: Part II
, 2010
"... Given a spatiotemporal network (ST network) whose edge properties vary with time, a timesubinterval minimum spanning tree (TSMST) is a collection of distinct minimum spanning trees of the ST network. The TSMST computation problem aims to identify a collection of distinct minimum spanning trees an ..."
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Given a spatiotemporal network (ST network) whose edge properties vary with time, a timesubinterval minimum spanning tree (TSMST) is a collection of distinct minimum spanning trees of the ST network. The TSMST computation problem aims to identify a collection of distinct minimum spanning trees and their respective timesubintervals under the constraint that the edge weight functions are piecewise linear. This is an important problem in ST network application domains such as wireless sensor networks (e.g., energy efficient routing). Computing TSMST is challenging because the ranking of candidate spanning trees is nonstationary over a given time interval. Existing methods such as dynamic graph algorithms and kinetic data structures assume separable edge weight functions. In contrast, this paper proposes novel algorithms to find TSMST for large ST networks by accounting for both separable and nonseparable piecewise linear edge weight functions. The algorithms are based on the ordering of edges in edgeorderintervals and intersection points of edge weight functions. 1
The weighted maximummean subtree and other bicriterion subtree problems
 In ACM Computing Research Repository
, 503
"... Abstract. We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the problem is trivially solved in linear time. When the ob ..."
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Abstract. We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the problem is trivially solved in linear time. When the objective is the sum of weights that are linear functions of a parameter, we show how to list all optima for all possible parameter values in O(n log n) time; this parametric optimization problem can be used to solve many bicriterion optimizations problems, in which each node has two values xi and yi associated with it, and the objective function is a bivariate function f ( ∑ xi, ∑ yi) of the sums of these two values. A special case, when f is the ratio of the two sums, is the Weighted MaximumMean Subtree Problem, or equivalently the Fractional PrizeCollecting Steiner Tree Problem on Trees; for this special case, we provide a linear time algorithm for this problem when all weights are positive, improving a previous O(n log n) solution, and prove that the problem is NPcomplete when negative weights are allowed. 1
Competitive Maintenance of Minimum Spanning Trees in Dynamic Graphs ⋆ Extended abstract
"... Abstract. We consider the problem of maintaining a minimum spanning tree within a graph with dynamically changing edge weights. An online algorithm is confronted with an input sequence of edge weight changes and has to choose a minimum spanning tree after each such change in the graph. The task of t ..."
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Abstract. We consider the problem of maintaining a minimum spanning tree within a graph with dynamically changing edge weights. An online algorithm is confronted with an input sequence of edge weight changes and has to choose a minimum spanning tree after each such change in the graph. The task of the algorithm is to perform as few changes in its minimum spanning tree as possible. We compare the number of changes in the minimum spanning tree produced by an online algorithm and that produced by an optimal offline algorithm. The number of changes is counted in the number of edges changed between spanning trees in consecutive rounds. For any graph with n vertices we provide a deterministic algorithm achieving a competitive ratio of O(n 2). We show that this result is optimal up to a constant. Furthermore we give a lower bound for randomized algorithms of Ω(log n). We show a randomized algorithm achieving a competitive ratio of O(n log n) for general graphs and O(log n) for planar graphs. 1
Finding the shortest bottleneck edge in a parametric minimum spanning tree
 In Proceedings of the 16th Annual ACMSIAM Symposium on Discrete Algorithms
, 2005
"... The result. Parametric optimization pwblems that concern graphs with continuously changing edge weights have been explored by numerous researctmrs, with motivation ranging fl'om sensitivity analysis to mobiledata applications. For instance, Dey [5] has shown that for an undirected graph with ..."
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The result. Parametric optimization pwblems that concern graphs with continuously changing edge weights have been explored by numerous researctmrs, with motivation ranging fl'om sensitivity analysis to mobiledata applications. For instance, Dey [5] has shown that for an undirected graph with n vertices and m edges where the edge weights are linear functions in one parameter ("time"), the minimum spanning tree (MST) can undergo at most O(mn 1/3) changes (edge swaps). Agarwal et al. [1] have given data structures to maintain the MST over time, with a cost of O(n 2/3 polylog n) per change. FernandezBaca et al. [7] have given an algorithm to compute all changes to the MST in O(mnlog n) total time. In this note, we focus on a problem studied by Katoh and Tokuyama [8]: Given a parametric graph with edge weights changing linearly in time, find the time value when the weight of the largest MST edge (the socalled bottleneck edge) is minimized. The bottleneck edge weight is of particular interest, because it represents a threshold for connectivity: it is equal to the smallest value r such that the subgraph of edges with weight < r stays connected. For this problem, Katoh and ~Ibkuyama [8] have given an O((ms/7nU7 + mn U3) polylogn) algorithm, which is faster than the current methods for computing all MSTs over time. Katoh and Tokuyama's method uses advanced ata structures for range searching and is therefore difficult to implement. Here, we give a much faster and simpler randomized algorithm that runs in O(n(m/n)Slogn + m) expected time for any fixed ¢> 0. This time bound is at least as good as 1 O(mlogn) and O(nlog + ~ n + m) for any fixed ~ '> 0, and almost matches an fi(n log n+m) lower bound. The new result is obtained by an interesting combination of techniques from computational geometry and graph data structures. The geometric aspects are similar to those used for the problem of 2d feasible linear programming with violations fi'om a previous paper [4].
Maintaining Approximate Minimum Steiner Tree and kcenter for Mobile Agents in a Sensor Network
"... Abstract—We study the problem of maintaining group communication between m mobile agents, tracked and helped by n static networked sensors. We develop algorithms to maintain a O(lg n)approximation to the minimum Steiner tree of the mobile agents such that the maintenance message cost is on average ..."
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Abstract—We study the problem of maintaining group communication between m mobile agents, tracked and helped by n static networked sensors. We develop algorithms to maintain a O(lg n)approximation to the minimum Steiner tree of the mobile agents such that the maintenance message cost is on average O(lg n) per each hop an agent moves. The key idea is to extract a ‘hierarchical wellseparated tree (HST) ’ on the sensor nodes such that the tree distance approximates the sensor network hop distance by a factor of O(lg n). We then prove that maintaining the subtree of the mobile agents on the HST uses logarithmic messages per hop movement. With the HST we can also maintain O(lg n) approximate kcenter for the mobile agents with the same message cost. Both the minimum Steiner tree and the kcenter problems are NPhard and our algorithms are the first efficient algorithms for maintaining approximate solutions in a distributed setting. I.
Sensing, Tracking, and Reasoning with Relations
, 2002
"... this paper is to present a methodology for planning and controlling the sensing, processing, and communication actions needed to accomplish a certain mission, while respecting the system resource constraints described above. To be concrete, consider two settings. Set1 is people moving around a build ..."
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this paper is to present a methodology for planning and controlling the sensing, processing, and communication actions needed to accomplish a certain mission, while respecting the system resource constraints described above. To be concrete, consider two settings. Set1 is people moving around a building; we are interested in security and surveillance applications, such as the detection of unusual activities and the monitoring of particular suspicious individuals. Set2 is a military engagement in an open terrain with a few buildings and ground enemy (e) and friendly (f ) vehicles moving in it; a commander must make key decisions that depend on the world state. In both settings, the sensor net needs to provide useful highlevel information to its clients
Robust, Efficient, and Accurate Contact Algorithms
, 2010
"... Robust, efficient, and accurate contact response remains a challenging problem in the simulation of deformable materials. Contact models should robustly handle contact between geometry by preventing interpenetrations. This should be accomplished while respecting natural laws in order to maintain phy ..."
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Robust, efficient, and accurate contact response remains a challenging problem in the simulation of deformable materials. Contact models should robustly handle contact between geometry by preventing interpenetrations. This should be accomplished while respecting natural laws in order to maintain physical correctness. We simultaneously desire to achieve these criteria as efficiently as possible to minimize simulation runtimes. Many methods exist that partially achieve these properties, but none yet fully attain all three. This thesis investigates existing methodologies with respect to these attributes, and proposes a novel algorithm for the simulation of deformable materials that demonstrate them all. This new method is analyzed and optimized, paving the way for future work in this simplified but
On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences\Lambda
, 2004
"... Abstract We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of times, the klevel has subquadratic (O(n2\Gamma 12s)) complexity. This answers one of the main open problems from the author's previous paper [Discrete ..."
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Abstract We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of times, the klevel has subquadratic (O(n2\Gamma 12s)) complexity. This answers one of the main open problems from the author's previous paper [Discrete Comput. Geom., 29:375393, 2003], which provided a weaker upper bound for a restricted class of curves only (graphs of degrees polynomials). When combined with existing tools (cutting curves, sampling, etc.), the new idea generates a slew of improved klevel results for most of the curve families studied earlier, including a nearO(n3=2) bound for parabolas.
50 MOTION
"... Motion is ubiquitous in the physical world, yet its study is much less developed than that of another common physical modality, namely shape. While we have several standardized mathematical shape descriptions, and even entire disciplines devoted to that area–such as ComputerAided Geometric Design ( ..."
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Motion is ubiquitous in the physical world, yet its study is much less developed than that of another common physical modality, namely shape. While we have several standardized mathematical shape descriptions, and even entire disciplines devoted to that area–such as ComputerAided Geometric Design (CAGD)—the