Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homol...
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In Connectivity Augmentation problems we are given a graph H= (V, EH) and an edge set E on V, and seek a min-size edge set J⊆ E such that H∪ J has larger edge/node connectivity than H. In the Edge-Connectivity A...
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k orthogonal line center problem computes a set of k axis-parallel lines for a given set of points in 2D such that the maximum among the distance between each point to its nearest line is minimized. A 2-factor approxi...
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We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that min...
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Given a k-vertex-connected graph G and a set S of extra edges (links), the goal of the k-vertex-connectivity augmentation problem is to find a subset S′ of S of minimum size such that adding S′ to G makes it (k+ 1 )...
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This article considers the problem of finding a shortest tour to visit viewing sets of points on a plane. Each viewing set is represented as an inverted view cone with apex angle alpha and height h. The apex of each c...
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This article considers the problem of finding a shortest tour to visit viewing sets of points on a plane. Each viewing set is represented as an inverted view cone with apex angle alpha and height h. The apex of each cone is restricted to lie on the ground plane. Its orientation angle (tilt) epsilon is the angle difference between the cone bisector and the ground plane normal. This is a novel variant of the 3D Traveling Salesman Problem with Neighborhoods (TSPN) called Cone-TSPN. One application of Cone-TSPN is to compute a trajectory to observe a given set of locations with a camera: for each location, we can generate a set of cones whose apex and orientation angles alpha and epsilon correspond to the camera's field of view and tilt. The height of each cone h corresponds to the desired resolution. Recently, Plonski and Isler presented an approximation algorithm for Cone-TSPN for the case where all cones have a uniform orientation angle of epsilon=0. We study a new variant of Cone-TSPN where we relax this constraint and allow the cones to have non-uniform orientations. We call this problem Tilted Cone-TSPN and present a polynomial-time approximation algorithm with ratio O(1+tan alpha 1-tan epsilon tan alpha(1+logmax(H)min(H))), where H is the set of all cone heights. We demonstrate through simulations that our algorithm can be implemented in a practical way and that by exploiting the structure of the cones we can achieve shorter tours. Finally, we present experimental results from various agriculture applications that show the benefit of considering view angles for path planning.
Graph routing problem (GRP) and its generalizations have been extensively studied because of their broad applications in the real world. In this paper, we study a variant of GRP called the general cluster routing prob...
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Graph parameters such as the diameter, radius, and vertex eccentricities are not defined in a useful way in Directed Acyclic Graphs (DAGs) using the standard measure of distance, since for any two nodes, there is no p...
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ISBN:
(纸本)9783959771955
Graph parameters such as the diameter, radius, and vertex eccentricities are not defined in a useful way in Directed Acyclic Graphs (DAGs) using the standard measure of distance, since for any two nodes, there is no path between them in one of the two directions. So it is natural to consider the distance between two nodes as the length of the shortest path in the direction in which this path exists, motivating the definition of the min-distance. The min-distance between two nodes u and v is the minimum of the shortest path distances from u to v and from v to u. As with the standard distance problems, the Strong Exponential Time Hypothesis [Impagliazzo- Paturi-Zane 2001, Calabro-Impagliazzo-Paturi 2009] leaves little hope for computing min-distance problems faster than computing All Pairs Shortest Paths, which can be solved in Õ(mn) time. So it is natural to resort to approximation algorithms in Õ(mn1-∈) time for some positive ∈. Abboud, Vassilevska W., and Wang [SODA 2016] first studied min-distance problems achieving constant factor approximation algorithms on DAGs, and Dalirrooyfard et al [ICALP 2019] gave the first constant factor approximation algorithms on general graphs for min-diameter, min-radius and min-eccentricities. Abboud et al obtained a 3-approximation algorithm for min-radius on DAGs which works in Õ(m√n) time, and showed that any (2 - δ)-approximation requires n2-o(1) time for any δ > 0, under the Hitting Set Conjecture. We close the gap, obtaining a 2-approximation algorithm which runs in Õ(m√n) time. As the lower bound of Abboud et al only works for sparse DAGs, we further show that our algorithm is conditionally tight for dense DAGs using a reduction from Boolean matrix multiplication. Moreover, Abboud et al obtained a linear time 2-approximation algorithm for min-diameter along with a lower bound stating that any (3/2 - δ)-approximation algorithm for sparse DAGs requires n2-o(1) time under SETH. We close this gap for dense DAGs by obtaining a 3/
In this paper, we study the maximum bounded connected bipartition problem (2-BCBP): given a vertex-weighted connected graph G= (V, E; w) and an upper bound B, the vertex set V is partitioned into two subsets denoted a...
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We study the minimum connected sensor cover problem (MIN-CSC) and the budgeted connected sensor cover (Budgeted-CSC) problem, both motivated by important applications (e.g., reduce the communication cost among sensors...
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We study the minimum connected sensor cover problem (MIN-CSC) and the budgeted connected sensor cover (Budgeted-CSC) problem, both motivated by important applications (e.g., reduce the communication cost among sensors) in wireless sensor networks. In both problems, we are given a set of sensors and a set of target points in the Euclidean plane. In MIN-CSC, our goal is to find a set of sensors of minimum cardinality, such that all target points are covered, and all sensors can communicate with each other (i.e., the communication graph is connected). We obtain a constant factor approximation algorithm, assuming that the ratio between the sensor radius and communication radius is bounded. In Budgeted-CSC problem, our goal is to choose a set of B sensors, such that the number of targets covered by the chosen sensors is maximized and the communication graph is connected. We also obtain a constant approximation under the same assumption. (C) 2020 Published by Elsevier B.V.
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