Approximation on the web: A compendium of NP optimization problems

Crescenzi, Pierluigi; Kann, Viggo

doi:10.1007/3-540-63248-4_10

Cited by 147 publications

(160 citation statements)

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“…Moreover, some nodes may have some chunks of the input data in prior. This is similar to Multiprocessor Scheduling [13], which is NP-Complete. We propose a greedy approach to find the optimal number of nodes based on the fact that, the T in equation 1 decreases first with the increase of parallelism, then starts to increase again [19].…”

Section: Mobile Mapreduce Designmentioning

confidence: 88%

Mobile MapReduce: Minimizing Response Time of Computing Intensive Mobile Applications

Hassan

Chen

2012

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Abstract. The increasing popularity of mobile devices calls for effective execution of mobile applications. A lot of research has been conducted on properly splitting and outsourcing computing intensive tasks to external resources (e.g., public clouds) by considering insufficient computing resources on mobile devices. However, little attention has been paid to the overall users' response time, where the network may dominate. In this study, we set to investigate how to effectively minimize users' response time for mobile applications. We consider both the impact of the network and the computing itself. We first show that outsourcing to nearby residential computers may be more advantageous than public clouds for mobile applications due to network impact. Furthermore, to speed up computing, we leverage parallel processing techniques. Accordingly, we propose to build Mobile MapReduce (MMR) to effectively execute outsource computing intensive mobile applications. Based on the original MapReduce framework, a new scheduling model is built in MMR that can always leverage the best computing resources to conduct computation with appropriate parallel processing. To demonstrate the performance of MMR, we run several real-world applications, such as text searching, face detection, and image processing, on the prototype. The results show great potentials of MMR in minimizing the response time of the outsourced mobile applications.

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Section: Mobile Mapreduce Designmentioning

confidence: 88%

Mobile MapReduce: Minimizing Response Time of Computing Intensive Mobile Applications

Hassan

Chen

2012

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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“…-For some constants c > c > 1, MAX2SAT can be approximated to ratio c [13], but not c [8]. -The problem of finding an optimal multi-processor scheduling with speed factors 6 has a PTAS, but no FPTAS [6,9].…”

Section: Hardness Of Approximationmentioning

confidence: 99%

“…6 This is the problem of scheduling tasks to processors of different speeds, while attempting to minimize execution time. Hence each task t in a set of tasks T has a length l(t), and each processor p in a set of processors P has a speed factor s(p).…”

Section: Theorem 5 Nc-sat(s K) ≤ Ac 0 M Ss(o(s + K) O(s + K))mentioning

confidence: 99%

Hardness of Approximation for Knapsack Problems

2014

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Hardness of approximation for Knapsack problemsBuhrman, H.M.; Loff, B.F.L.; Torenvliet, L. Published in: Theory of Computing Systems DOI:10.1007/s00224-014-9550-z Link to publication Citation for published version (APA):Buhrman, H., Loff, B., & Torenvliet, L. (2015). Hardness of approximation for Knapsack problems. Theory of Computing Systems, 56(2), 372-393. DOI: 10.1007/s00224-014-9550-z General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Abstract We show various hardness results for knapsack and related problems; in particular we will show that unless the Exponential-Time Hypothesis is false, subsetsum cannot be approximated any better than with an FPTAS. We also provide new unconditional lower bounds for approximating knapsack in Ketan Mulmuley's parallel PRAM model. Furthermore, we give a simple new algorithm for approximating knapsack and subset-sum, that can be adapted to work for small space, or in small parallel time.

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“…It involves the design of a set of minimum cost vehicle trips, originating and ending at a depot, for a fleet of vehicles with loading capacity that services a set of client spots with required demands. The problems studied in this chapter can be described in the style used by Crescenzi & Kann (Crescenzi & Kann, 2000) for their compendium of NP optimization problems. Although VRP is not listed in the compendium, it is given by Prins & Bouchenoua (Prins & Bouchenoua, 2004) as follows.…”

Section: Vehicle Routing Problem (Vrp)mentioning

confidence: 99%