6 research outputs found

    Online load balancing with general reassignment cost

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    We investigate a semi-online variant of load balancing with restricted assignment. In this problem, we are given n jobs, which need to be processed by m machines with the goal to minimize the maximum machine load. Since strong lower bounds rule out any competitive ratio of o(logโกn), we may reassign jobs at a certain job-individual cost. We generalize a result by Gupta, Kumar, and Stein (SODA 2014) by giving a O(logโกlogโกmn)-competitive algorithm with constant amortized reassignment cost

    Online Advertising Assignment Problems Considering Realistic Constraints

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    ํ•™์œ„๋…ผ๋ฌธ (๋ฐ•์‚ฌ) -- ์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› : ๊ณต๊ณผ๋Œ€ํ•™ ์‚ฐ์—…๊ณตํ•™๊ณผ, 2020. 8. ๋ฌธ์ผ๊ฒฝ.With a drastic increase in online communities, many companies have been paying attention to online advertising. The main advantages of online advertising are traceability, cost-effectiveness, reachability, and interactivity. The benefits facilitate the continuous popularity of online advertising. For Internet-based companies, a well-constructed online advertisement assignment increases their revenue. Hence, the managers need to develop their decision-making processes for assigning online advertisements on their website so that their revenue is maximized. In this dissertation, we consider online advertising assignment problems considering realistic constraints. There are three types of online advertising assignment problems: (i) Display ads problem in adversarial order, (ii) Display ads problem in probabilistic order, and (iii) Online banner advertisement scheduling for advertising effectiveness. Unlike previous assignment problems, the problems are pragmatic approaches that reflect realistic constraints and advertising effectiveness. Moreover, the algorithms the dissertation designs offer important insights into the online advertisement assignment problem. We give a brief explanation of the fundamental methodologies to solve the online advertising assignment problems in Chapter 1. At the end of this chapter, the contributions and outline of the dissertation are also presented. In Chapter 2, we propose the display ads problem in adversarial order. Deterministic algorithms with worst-case guarantees are designed, and the competitive ratios of them are presented. Upper bounds for the problem are also proved. We investigate the display ads problem in probabilistic order in Chapter 3. This chapter presents stochastic online algorithms with scenario-based stochastic programming and Benders decomposition for two probabilistic order models. In Chapter 4, an online banner advertisement scheduling model for advertising effectiveness is designed. We also present the solution methodologies used to obtain valid lower and upper bounds of the model efficiently. Chapter 5 offers conclusions and suggestion for future studies. The approaches to solving the problems are meaningful in both academic and industrial areas. We validate these approaches can solve the problems efficiently and effectively by conducting computational experiments. The models and solution methodologies are expected to be convenient and beneficial when managers at Internet-based companies place online advertisements on their websites.์˜จ๋ผ์ธ ์ปค๋ฎค๋‹ˆํ‹ฐ์˜ ๊ธ‰๊ฒฉํ•œ ์„ฑ์žฅ์— ๋”ฐ๋ผ, ๋งŽ์€ ํšŒ์‚ฌ๋“ค์ด ์˜จ๋ผ์ธ ๊ด‘๊ณ ์— ๊ด€์‹ฌ์„ ๊ธฐ์šธ์ด๊ณ  ์žˆ๋‹ค. ์˜จ๋ผ์ธ ๊ด‘๊ณ ์˜ ์žฅ์ ์œผ๋กœ๋Š” ์ถ”์  ๊ฐ€๋Šฅ์„ฑ, ๋น„์šฉ ํšจ๊ณผ์„ฑ, ๋„๋‹ฌ ๊ฐ€๋Šฅ์„ฑ, ์ƒํ˜ธ์ž‘์šฉ์„ฑ ๋“ฑ์ด ์žˆ๋‹ค. ์˜จ๋ผ์ธ์— ๊ธฐ๋ฐ˜์„ ๋‘๋Š” ํšŒ์‚ฌ๋“ค์€ ์ž˜ ์งœ์—ฌ์ง„ ์˜จ๋ผ์ธ ๊ด‘๊ณ  ํ• ๋‹น๊ฒฐ์ •์— ๊ด€์‹ฌ์„ ๋‘๊ณ  ์žˆ๊ณ , ์ด๋Š” ๊ด‘๊ณ  ์ˆ˜์ต๊ณผ ์—ฐ๊ด€๋  ์ˆ˜ ์žˆ๋‹ค. ๋”ฐ๋ผ์„œ ์˜จ๋ผ์ธ ๊ด‘๊ณ  ๊ด€๋ฆฌ์ž๋Š” ์ˆ˜์ต์„ ๊ทน๋Œ€ํ™” ํ•  ์ˆ˜ ์žˆ๋Š” ์˜จ๋ผ์ธ ๊ด‘๊ณ  ํ• ๋‹น ์˜์‚ฌ ๊ฒฐ์ • ํ”„๋กœ์„ธ์Šค๋ฅผ ๊ฐœ๋ฐœํ•˜์—ฌ์•ผ ํ•œ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” ํ˜„์‹ค์ ์ธ ์ œ์•ฝ์„ ๊ณ ๋ คํ•œ ์˜จ๋ผ์ธ ๊ด‘๊ณ  ํ• ๋‹น ๋ฌธ์ œ๋“ค์„ ์ œ์•ˆํ•œ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ ๋‹ค๋ฃจ๋Š” ๋ฌธ์ œ๋Š” (1) adversarial ์ˆœ์„œ๋กœ ์ง„ํ–‰ํ•˜๋Š” ๋””์Šคํ”Œ๋ ˆ์ด ์• ๋“œ๋ฌธ์ œ, (2) probabilistic ์ˆœ์„œ๋กœ ์ง„ํ–‰ํ•˜๋Š” ๋””์Šคํ”Œ๋ ˆ์ด ์• ๋“œ๋ฌธ์ œ ๊ทธ๋ฆฌ๊ณ  (3) ๊ด‘๊ณ ํšจ๊ณผ๋ฅผ ์œ„ํ•œ ์˜จ๋ผ์ธ ๋ฐฐ๋„ˆ ๊ด‘๊ณ  ์ผ์ •๊ณ„ํš์ด๋‹ค. ์ด์ „์— ์ œ์•ˆ๋˜์—ˆ๋˜ ๊ด‘๊ณ  ํ• ๋‹น ๋ฌธ์ œ๋“ค๊ณผ ๋‹ฌ๋ฆฌ, ๋ณธ ๋…ผ๋ฌธ์—์„œ ์ œ์•ˆํ•œ ๋ฌธ์ œ๋“ค์€ ํ˜„์‹ค์ ์ธ ์ œ์•ฝ๊ณผ ๊ด‘๊ณ ํšจ๊ณผ๋ฅผ ๋ฐ˜์˜ํ•˜๋Š” ์‹ค์šฉ์ ์ธ ์ ‘๊ทผ ๋ฐฉ์‹์ด๋‹ค. ๋˜ํ•œ ์ œ์•ˆํ•˜๋Š” ์•Œ๊ณ ๋ฆฌ์ฆ˜์€ ์˜จ๋ผ์ธ ๊ด‘๊ณ  ํ• ๋‹น ๋ฌธ์ œ์˜ ์šด์˜๊ด€๋ฆฌ์— ๋Œ€ํ•œ ํ†ต์ฐฐ๋ ฅ์„ ์ œ๊ณตํ•œ๋‹ค. 1์žฅ์—์„œ๋Š” ์˜จ๋ผ์ธ ๊ด‘๊ณ  ํ• ๋‹น ๋ฌธ์ œ์— ๋Œ€ํ•œ ๋ฌธ์ œํ•ด๊ฒฐ ๋ฐฉ๋ฒ•๋ก ์— ๋Œ€ํ•ด ๊ฐ„๋‹จํžˆ ์†Œ๊ฐœํ•œ๋‹ค. ๋”๋ถˆ์–ด ์—ฐ๊ตฌ์˜ ๊ธฐ์—ฌ์™€ ๊ฐœ์š”๋„ ์ œ๊ณต๋œ๋‹ค. 2์žฅ์—์„œ๋Š” adversarial ์ˆœ์„œ๋กœ ์ง„ํ–‰ํ•˜๋Š” ๋””์Šคํ”Œ๋ ˆ์ด ์• ๋“œ๋ฌธ์ œ๋ฅผ ์ œ์•ˆํ•œ๋‹ค. worst-case๋ฅผ ๋ณด์žฅํ•˜๋Š” ๊ฒฐ์ •๋ก ์  ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์„ค๊ณ„ํ•˜๊ณ , ์ด๋“ค์˜ competitive ratio๋ฅผ ์ฆ๋ช…ํ•œ๋‹ค. ๋”๋ถˆ์–ด ๋ฌธ์ œ์˜ ์ƒํ•œ๋„ ์ž…์ฆ๋œ๋‹ค. 3์žฅ์—์„œ๋Š” probabilistic ์ˆœ์„œ๋กœ ์ง„ํ–‰ํ•˜๋Š” ๋””์Šคํ”Œ๋ ˆ์ด ์• ๋“œ๋ฌธ์ œ๋ฅผ ์ œ์•ˆํ•œ๋‹ค. ์‹œ๋‚˜๋ฆฌ์˜ค ๊ธฐ๋ฐ˜์˜ ํ™•๋ฅ ๋ก ์  ์˜จ๋ผ์ธ ์•Œ๊ณ ๋ฆฌ์ฆ˜๊ณผ Benders ๋ถ„ํ•ด๋ฐฉ๋ฒ•์„ ํ˜ผํ•ฉํ•œ ์ถ”๊ณ„ ์˜จ๋ผ์ธ ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์ œ์‹œํ•œ๋‹ค. 4์žฅ์—์„œ๋Š” ๊ด‘๊ณ ํšจ๊ณผ๋ฅผ ์œ„ํ•œ ์˜จ๋ผ์ธ ๋ฐฐ๋„ˆ ๊ด‘๊ณ  ์ผ์ •๊ณ„ํš์„ ์„ค๊ณ„ํ•œ๋‹ค. ๋˜ํ•œ, ๋ชจ๋ธ์˜ ์œ ํšจํ•œ ์ƒํ•œ๊ณผ ํ•˜ํ•œ์„ ํšจ์œจ์ ์œผ๋กœ ์–ป๋Š” ๋ฐ ์‚ฌ์šฉ๋˜๋Š” ๋ฌธ์ œํ•ด๊ฒฐ ๋ฐฉ๋ฒ•๋ก ์„ ์ œ์•ˆํ•œ๋‹ค. 5์žฅ์—์„œ๋Š” ๋ณธ ๋…ผ๋ฌธ์˜ ๊ฒฐ๋ก ๊ณผ ํ–ฅํ›„ ์—ฐ๊ตฌ๋ฅผ ์œ„ํ•œ ๋ฐฉํ–ฅ์„ ์ œ๊ณตํ•œ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ ์ œ์•ˆํ•˜๋Š” ๋ฌธ์ œํ•ด๊ฒฐ ๋ฐฉ๋ฒ•๋ก ์€ ํ•™์ˆ  ๋ฐ ์‚ฐ์—… ๋ถ„์•ผ ๋ชจ๋‘ ์˜๋ฏธ๊ฐ€ ์žˆ๋‹ค. ์ˆ˜์น˜ ์‹คํ—˜์„ ํ†ตํ•ด ๋ฌธ์ œํ•ด๊ฒฐ ์ ‘๊ทผ ๋ฐฉ์‹์ด ๋ฌธ์ œ๋ฅผ ํšจ์œจ์ ์ด๊ณ  ํšจ๊ณผ์ ์œผ๋กœ ํ•ด๊ฒฐํ•  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์ธ๋‹ค. ์ด๋Š” ์˜จ๋ผ์ธ ๊ด‘๊ณ  ๊ด€๋ฆฌ์ž๊ฐ€ ๋ณธ ๋…ผ๋ฌธ์—์„œ ์ œ์•ˆํ•˜๋Š” ๋ฌธ์ œ์™€ ๋ฌธ์ œํ•ด๊ฒฐ ๋ฐฉ๋ฒ•๋ก ์„ ํ†ตํ•ด ์˜จ๋ผ์ธ ๊ด‘๊ณ  ํ• ๋‹น๊ด€๋ จ ์˜์‚ฌ๊ฒฐ์ •์„ ์ง„ํ–‰ํ•˜๋Š” ๋ฐ ์žˆ์–ด ๋„์›€์ด ๋  ๊ฒƒ์œผ๋กœ ๊ธฐ๋Œ€ํ•œ๋‹ค.Chapter 1 Introduction 1 1.1 Display Ads Problem 3 1.1.1 Online Algorithm 4 1.2 Online Banner Advertisement Scheduling Problem 5 1.3 Research Motivations and Contributions 6 1.4 Outline of the Dissertation 9 Chapter 2 Online Advertising Assignment Problem in Adversarial Order 12 2.1 Problem Description and Literature Review 12 2.2 Display Ads Problem in Adversarial Order 15 2.3 Deterministic Algorithms for Adversarial Order 17 2.4 Upper Bounds of Deterministic Algorithms for Adversarial Order 22 2.5 Summary 28 Chapter 3 Online Advertising Assignment Problem in Probabilistic Order 30 3.1 Problem Description and Literature Review 30 3.2 Display Ads Problem in Probabilistic Order 33 3.3 Stochastic Online Algorithms for Probabilistic Order 34 3.3.1 Two-Stage Stochastic Programming 35 3.3.2 Known IID model 37 3.3.3 Random permutation model 41 3.3.4 Stochastic approach using primal-dual algorithm 45 3.4 Computational Experiments 48 3.4.1 Results for known IID model 55 3.4.2 Results for random permutation model 57 3.4.3 Managerial insights for Algorithm 3.1 59 3.5 Summary 60 Chapter 4 Online Banner Advertisement Scheduling for Advertising Effectiveness 61 4.1 Problem Description and Literature Review 61 4.2 Mathematical Model 68 4.2.1 Objective function 68 4.2.2 Notations and formulation 72 4.3 Solution Methodologies 74 4.3.1 Heuristic approach to finding valid lower and upper bounds 75 4.3.2 Hybrid tabu search 79 4.4 Computational Experiments 80 4.4.1 Results for problems with small data sets 82 4.4.2 Results for problems with large data sets 84 4.4.3 Results for problems with standard data 86 4.4.4 Managerial insights for the results 90 4.5 Summary 92 Chapter 5 Conclusions and Future Research 93 Appendices 97 A Initial Sequence of the Hybrid Tabu Search 98 B Procedure of the Hybrid Tabu Search 99 C Small Example of the Hybrid Tabu Search 101 D Linearization Technique of Bilinear Form in R2 104 Bibliography 106Docto
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