scholarly journals Weighted Cache Location Problem with Identical Servers

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Hongfa Wang ◽  
Wei Ding
Keyword(s):  
Parallel Algorithm ◽  
Numerical Experiments ◽  
Location Problem ◽  
Exact Algorithm ◽  
Worst Case ◽  
Shortest Route ◽  
General Network ◽  
Cache Location

This paper extends the well-knownp-CLP with one server top-CLP withm≥2identical servers, denoted by(p,m)-CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate(p,m)-CLP under CSOP to(p,m)-CSOP CLP and investigate that(p,m)-CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case ofm=2is the focus of this paper. We first devise an improvedO(ph2+n)-time parallel exact algorithm forp-CLP on a tree and then present a parallel exact algorithm with at mostO((4/9)p2n2)time in the worst case for(p,2)-CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases ofm>2to obtain a worst-caseO((4/9)(n-m)2((m+p)p/p-1!))-time exact algorithm. At the end of the paper, we first give an example to illustrate our algorithms and then make a series of numerical experiments to compare the running times of our algorithms.

scholarly journals Stochastic Flips on Dimer Tilings

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Triangular Grid ◽  
Expected Number ◽  
Worst Case ◽  
Average Case ◽  
International Audience

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.

Fast closed testing for exchangeable local tests

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 761-768 ◽  
Author(s):  
E Dobriban
Keyword(s):  
Error Rate ◽  
Multiple Testing ◽  
Exact Algorithm ◽  
Multiple Hypothesis Testing ◽  
Test Statistics ◽  
Familywise Error Rate ◽  
Closure Principle ◽  
Worst Case ◽  
Higher Criticism ◽  
False Discovery

Summary Multiple hypothesis testing problems arise naturally in science. This note introduces a new fast closed testing method for multiple testing which controls the familywise error rate. Controlling the familywise error rate is state-of-the-art in many important application areas and is preferred over false discovery rate control for many reasons, including that it leads to stronger reproducibility. The closure principle rejects an individual hypothesis if all global nulls of subsets containing it are rejected using some test statistics. It takes exponential time in the worst case. When the tests are symmetric and monotone, the proposed method is an exact algorithm for computing the closure, is quadratic in the number of tests, and is linear in the number of discoveries. Our framework generalizes most examples of closed testing, such as Holm’s method and the Bonferroni method. As a special case of the method, we propose the Simes and higher criticism fusion test, which is powerful both for detecting a few strong signals and for detecting many moderate signals.

scholarly journals On Rectilinear Distance-Preserving Trees

VLSI Design ◽  
1998 ◽  
Vol 7 (1) ◽  
pp. 15-30
Author(s):  
Gustavo E. Téllez ◽  
Majid Sarrafzadeh
Keyword(s):  
Approximation Algorithm ◽  
Heuristic Algorithm ◽  
Time Complexity ◽  
High Performance ◽  
Exact Algorithm ◽  
Wire Length ◽  
Worst Case ◽  
Rectilinear Distance ◽  
Source To Sink ◽  
Linear Delay

Given a set of terminals on the plane N={s,ν1,…,νn}, with a source terminal s, a Rectilinear Distance-Preserving Tree (RDPT) T(V, E) is defined as a tree rooted at s, connecting all terminals in N. An RDPT has the property that the length of every source to sink path is equal to the rectilinear distance between that source and sink. A Min- Cost Rectilinear Distance-Preserving Tree (MRDPT) minimizes the total wire length while maintaining minimal source to sink linear delay, making it suitable for high performance interconnect applications.This paper studies problems in the construction of RDPTs, including the following contributions. A new exact algorithm for a restricted version of the problem in one quadrant with O(n2) time complexity is proposed. A novel heuristic algorithm, which uses optimally solvable sub-problems, is proposed for the problem in a single quadrant. The average and worst-case time complexity for the proposed heuristic algorithm are O(n3/2) and O(n3), respectively. A 2-approximation of the quadrant merging problem is proposed. The proposed algorithm has time complexity O(α2T(n)+α3) for any constant α > 1, where T(n) is the time complexity of the solution of the RDPT problem on one quadrant. This result improves over the best previous quadrant merging solution which has O(n2T(n)+n3) time complexity.We test our algorithms on randomly uniform point sets and compare our heuristic RDPT construction against a Minimum Cost Rectilinear Steiner (MRST) tree approximation algorithm. Our results show that RDPTs are competitive with Steiner trees in total wire-length when the number of terminals is less than 32. This result makes RDPTs suitable for VLSI routing applications. We also compare our algorithm to the Rao-Shor RDPT approximation algorithm obtaining improvements of up to 10% in total wirelength. These comparisons show that the algorithms proposed herein produce promising results.

scholarly journals Optimal online algorithms for the portfolio selection problem, bi-directional trading and -search with interrelated prices

2019 ◽  
Vol 53 (2) ◽  
pp. 559-576 ◽  
Author(s):  
Pascal Schroeder ◽  
Imed Kacem ◽  
Günter Schmidt
Keyword(s):  
Portfolio Selection ◽  
Online Algorithms ◽  
Competitive Ratio ◽  
Numerical Experiments ◽  
Input Sequence ◽  
Relative Price ◽  
Selection Problem ◽  
Online Search ◽  
Worst Case ◽  
Portfolio Selection Problem

In this work we investigate the portfolio selection problem (P1) and bi-directional trading (P2) when prices are interrelated. Zhang et al. (J. Comb. Optim. 23 (2012) 159–166) provided the algorithm UND which solves one variant of P2. We are interested in solutions which are optimal from a worst-case perspective. For P1, we prove the worst-case input sequence and derive the algorithm optimal portfolio for interrelated prices (OPIP). We then prove the competitive ratio and optimality. We use the idea of OPIP to solve P2 and derive the algorithm called optimal conversion for interrelated prices (OCIP). Using OCIP, we also design optimal online algorithms for bi-directional search (P3) called bi-directional UND (BUND) and optimal online search for unknown relative price bounds (RUN). We run numerical experiments and conclude that OPIP and OCIP perform well compared to other algorithms even if prices do not behave adverse.

The Cache Location Problem

2004 ◽  
pp. 67-98
Author(s):  
Cheng Jin ◽  
Sugih Jamin ◽  
Danny Raz ◽  
Yuval Shavitt
Keyword(s):  
Location Problem ◽  
Cache Location

scholarly journals Facility Location Problem Approach for Distributed Drones

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 118 ◽  
Author(s):  
Jared Lynskey ◽  
Kyi Thar ◽  
Thant Oo ◽  
Choong Hong
Keyword(s):  
Energy Consumption ◽  
Facility Location ◽  
Location Problem ◽  
Average Distance ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Traveling Salesman ◽  
Future Research ◽  
Shortest Route ◽  
Initial Location

Currently, industry and academia are undergoing an evolution in developing the next generation of drone applications. Including the development of autonomous drones that can carry out tasks without the assistance of a human operator. In spite of this, there are still problems left unanswered related to the placement of drone take-off, landing and charging areas. Future policies by governments and aviation agencies are inevitably going to restrict the operational area where drones can take-off and land. Hence, there is a need to develop a system to manage landing and take-off areas for drones. Additionally, we proposed this approach due to the lack of justification for the initial location of drones in current research. Therefore, to provide a foundation for future research, we give a justified reason that allows predetermined location of drones with the use of drone ports. Furthermore, we propose an algorithm to optimally place these drone ports to minimize the average distance drones must travel based on a set of potential drone port locations and tasks generated in a given area. Our approach is derived from the Facility Location problem which produces an efficient near optimal solution to place drone ports that reduces the overall drone energy consumption. Secondly, we apply various traveling salesman algorithms to determine the shortest route the drone must travel to visit all the tasks.

scholarly journals Adaptive cubic regularization methods with dynamic inexact Hessian information and applications to finite-sum minimization

2020 ◽  
Author(s):  
Stefania Bellavia ◽  
Gianmarco Gurioli ◽  
Benedetta Morini
Keyword(s):  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
Regularization Methods ◽  
Worst Case ◽  
Nonconvex Optimization Problems ◽  
New Variant ◽  
Cubic Regularization ◽  
Finite Sum

Abstract We consider the adaptive regularization with cubics approach for solving nonconvex optimization problems and propose a new variant based on inexact Hessian information chosen dynamically. The theoretical analysis of the proposed procedure is given. The key property of ARC framework, constituted by optimal worst-case function/derivative evaluation bounds for first- and second-order critical point, is guaranteed. Application to large-scale finite-sum minimization based on subsampled Hessian is discussed and analyzed in both a deterministic and probabilistic manner, and equipped with numerical experiments on synthetic and real datasets.

scholarly journals An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Ľuboš Buzna ◽  
Michal Koháni ◽  
Jaroslav Janáček
Keyword(s):  
Approximation Algorithm ◽  
Facility Location ◽  
Location Problem ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Exact Algorithm ◽  
General Purpose ◽  
Median Problem ◽  
Discrete Facility Location ◽  
Number Of Customers

We present a new approximation algorithm to the discrete facility location problem providing solutions that are close to the lexicographic minimax optimum. The lexicographic minimax optimum is a concept that allows to find equitable location of facilities serving a large number of customers. The algorithm is independent of general purpose solvers and instead uses algorithms originally designed to solve thep-median problem. By numerical experiments, we demonstrate that our algorithm allows increasing the size of solvable problems and provides high-quality solutions. The algorithm found an optimal solution for all tested instances where we could compare the results with the exact algorithm.

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