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Randomized Algorithms for Geometric Optimization Problems
Pankaj K. Agarwal,Sandeep Sen +1 more
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This chapter reviews randomization algorithms developed in the last few years to solve a wide range of geometric optimization problems, including facility location, proximity problems, nearest neighbor searching, statistical estimators, and Euclidean TSP.Abstract:
This chapter reviews randomization algorithms developed in the last few years to solve a wide range of geometric optimization problems. We review a number of general techniques, including randomized binary search, randomized linear-programming algorithms, and random sampling. Next, we describe several applications of these techniques, including facility location, proximity problems, nearest neighbor searching, statistical estimators, and Euclidean TSP. Work by the rst author was supported by Army Research O ce MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by NSF grants EIA{9870724, EIA{997287, and CCR{9732787, and by a grant from the U.S.-Israeli Binational Science Foundation. Center for Geometric Computing, Department of Computer Science, Box 90129, Duke University, Durham, NC 27708-0129, USA. E-mail: pankaj@cs.duke.edu Department of Computer Science and Engineering, IIT Delhi, New Delhi 110016, India. Email:ssen@cse.iitd.ernet.inread more
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Distributed Abstract Optimization via Constraints Consensus: Theory and Applications
TL;DR: In this paper, constraints consensus algorithms for distributed abstract programs with guaranteed finite-time convergence to a global optimum are proposed for networks with weak time-dependent connectivity requirements and tight memory constraints.
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Distributed Abstract Optimization via Constraints Consensus: Theory and Applications
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Distributed Optimization for Smart Cyber-Physical Networks
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Almost tight upper bounds for vertical decompositions in four dimensions
TL;DR: It is shown that the complexity of the vertical decomposition of an arrangement of n fixed-degree algebraic surfaces or surface patches in four dimensions is O(n/sup 4+/spl epsi//) for any /spl ePSi/ > 0, which improves the best previously known upper bound for this problem by a near-linear factor, and settles a major problem in the theory of arrangements of surfaces.
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