Approximation Algorithms for the Star k-Hub Center Problem in Metric Graphs

2016 ◽  
pp. 222-234 ◽  
Author(s):  
Li-Hsuan Chen ◽  
Dun-Wei Cheng ◽  
Sun-Yuan Hsieh ◽  
Ling-Ju Hung ◽  
Chia-Wei Lee ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Center Problem ◽  
Metric Graphs

scholarly journals Approximation Algorithms for the Vertex K-Center Problem: Survey and Experimental Evaluation

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 109228-109245 ◽  
Author(s):  
Jesus Garcia-Diaz ◽  
Rolando Menchaca-Mendez ◽  
Ricardo Menchaca-Mendez ◽  
Saul Pomares Hernandez ◽  
Julio Cesar Perez-Sansalvador ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Experimental Evaluation ◽  
Center Problem

scholarly journals Approximation algorithms for the p-hub center routing problem in parameterized metric graphs

2020 ◽  
Vol 806 ◽  
pp. 271-280 ◽  
Author(s):  
Li-Hsuan Chen ◽  
Sun-Yuan Hsieh ◽  
Ling-Ju Hung ◽  
Ralf Klasing
Keyword(s):  
Approximation Algorithms ◽  
Metric Graphs ◽  
Routing Problem

THE ALIGNED K-CENTER PROBLEM

2011 ◽  
Vol 21 (02) ◽  
pp. 157-178 ◽  
Author(s):  
PETER BRASS ◽  
CHRISTIAN KNAUER ◽  
HYEON-SUK NA ◽  
CHAN-SU SHIN ◽  
ANTOINE VIGNERON
Keyword(s):  
Approximation Algorithms ◽  
Randomized Algorithms ◽  
Randomized Algorithm ◽  
Time Algorithm ◽  
Center Problem ◽  
Running Time ◽  
Maximum Radius ◽  
Arbitrary Line ◽  
Set Of Points

In this paper we study several instances of the alignedk-center problem where the goal is, given a set of points S in the plane and a parameter k ⩾ 1, to find k disks with centers on a line ℓ such that their union covers S and the maximum radius of the disks is minimized. This problem is a constrained version of the well-known k-center problem in which the centers are constrained to lie in a particular region such as a segment, a line, or a polygon. We first consider the simplest version of the problem where the line ℓ is given in advance; we can solve this problem in time O(n log 2 n). In the case where only the direction of ℓ is fixed, we give an O(n2 log 2 n)-time algorithm. When ℓ is an arbitrary line, we give a randomized algorithm with expected running time O(n4 log 2 n). Then we present (1+ε)-approximation algorithms for these three problems. When we denote T(k, ε) = (k/ε2+(k/ε) log k) log (1/ε), these algorithms run in O(n log k + T(k, ε)) time, O(n log k + T(k, ε)/ε) time, and O(n log k + T(k, ε)/ε2) time, respectively. For k = O(n1/3/ log n), we also give randomized algorithms with expected running times O(n + (k/ε2) log (1/ε)), O(n+(k/ε3) log (1/ε)), and O(n + (k/ε4) log (1/ε)), respectively.

Approximation Algorithms for Submodular Data Summarization with a Knapsack Constraint

2021 ◽  
Vol 5 (1) ◽  
pp. 1-31
Author(s):  
Kai Han ◽  
Shuang Cui ◽  
Tianshuai Zhu ◽  
Enpei Zhang ◽  
Benwei Wu ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Fundamental Problem ◽  
Randomized Algorithm ◽  
Deterministic Algorithm ◽  
Submodular Function ◽  
Approximation Ratio ◽  
Performance Bounds ◽  
Data Summarization ◽  
Submodular Optimization ◽  
Knapsack Constraint

Data summarization, i.e., selecting representative subsets of manageable size out of massive data, is often modeled as a submodular optimization problem. Although there exist extensive algorithms for submodular optimization, many of them incur large computational overheads and hence are not suitable for mining big data. In this work, we consider the fundamental problem of (non-monotone) submodular function maximization with a knapsack constraint, and propose simple yet effective and efficient algorithms for it. Specifically, we propose a deterministic algorithm with approximation ratio 6 and a randomized algorithm with approximation ratio 4, and show that both of them can be accelerated to achieve nearly linear running time at the cost of weakening the approximation ratio by an additive factor of ε. We then consider a more restrictive setting without full access to the whole dataset, and propose streaming algorithms with approximation ratios of 8+ε and 6+ε that make one pass and two passes over the data stream, respectively. As a by-product, we also propose a two-pass streaming algorithm with an approximation ratio of 2+ε when the considered submodular function is monotone. To the best of our knowledge, our algorithms achieve the best performance bounds compared to the state-of-the-art approximation algorithms with efficient implementation for the same problem. Finally, we evaluate our algorithms in two concrete submodular data summarization applications for revenue maximization in social networks and image summarization, and the empirical results show that our algorithms outperform the existing ones in terms of both effectiveness and efficiency.

scholarly journals On the nonlinear Dirac equation on noncompact metric graphs

2021 ◽  
Vol 278 ◽  
pp. 326-357
Author(s):  
William Borrelli ◽  
Raffaele Carlone ◽  
Lorenzo Tentarelli
Keyword(s):  
Dirac Equation ◽  
Metric Graphs ◽  
Nonlinear Dirac Equation
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