6 research outputs found

    Push-Pull Block Puzzles are Hard

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    This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question by Zubaran and Ritt. Push-pull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a `robot' on a square grid with 1ร—11 \times 1 obstacles. The obstacles cannot be traversed by the robot, but some can be pushed and pulled by the robot into adjacent squares. Thin walls prevent movement between two adjacent squares. This work follows in a long line of algorithms and complexity work on similar problems. The 2D push-pull block puzzle shows up in the video games Pukoban as well as The Legend of Zelda: A Link to the Past, giving another proof of hardness for the latter. This variant of block-pushing puzzles is of particular interest because of its connections to reversibility, since any action (e.g., push or pull) can be inverted by another valid action (e.g., pull or push).Comment: Full version of CIAC 2017 paper. 17 page

    Push-Pull boundary optimization problem of special steel industry to improve customer service level

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    ํ•™์œ„๋…ผ๋ฌธ (์„์‚ฌ)-- ์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› ๊ณต๊ณผ๋Œ€ํ•™ ์‚ฐ์—…๊ณตํ•™๊ณผ, 2017. 8. ํ™์„ฑํ•„.The steel industry is divided into the Integrated Steel Mill Industry(ISM) and Special Steel Mill Industry(SSM). ISM is easy to apply push-pull hybrid strategy, whereas for the SSM only the Pull strategy has been considered. In this paper, we consider push-pull boundary optimization problem to reduce costs and improve customer service level. As a representative hybrid strategy, the delayed differentiation strategy is based on inventory of common semi-finished products. It means that if the actual demand arrives, it will be supplied through the remaining processes. In this study, first, we derived semi-finished products through the analysis of product, raw material, product processes, and define the problem of inventory management of semi-finished products to achieve push-pull border optimization. Specifically, the problem of semi-finished goods inventory management is deciding target inventory and the replenishment cycle. This problem is similar with the Joint Replenishment Problem (JRP), where both problems are finding multiple cycle makes the problem difficult. Therefore, Solve problems through heuristics. JRP, known as NP-hard, fixes the problem by fixing the period to a constant value. In this model, similarly, the period is fixed by multiplier of 2, power-of-two policy. Introduction of semi-finished products through experiments, the cost was reduced compared to before.์ฒ ๊ฐ•์‚ฐ์—…์€ ์ผ๊ด€์ œ์ฒ ์‚ฐ์—…(Integrated Steel Mill Industry, ISM)๊ณผ ํŠน์ˆ˜๊ฐ• ์‚ฐ์—…(Special Steel Mill Industry, SSM)์œผ๋กœ ๊ตฌ๋ถ„๋œ๋‹ค. ISM์€ push-pull ํ˜ผํ•ฉ ์ „๋žต์„ ์ ์šฉํ•˜๊ธฐ ์šฉ์ดํ•œ๋ฐ ๋น„ํ•ด SSM์€ ์ˆœ์ˆ˜ํ•œ pull ๋ฐฉ์‹์ด ์ตœ์„ ์ด๋ผ๊ณ  ์—ฌ๊ฒจ์ ธ์™”๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” SSM์„ ๋Œ€์ƒ์œผ๋กœ ๋น„์šฉ ์ ˆ๊ฐ ๋ฐ ๊ณ ๊ฐ ์„œ๋น„์Šค ํ–ฅ์ƒ์„ ์œ„ํ•œ ํ˜ผํ•ฉ ์ „๋žต์˜ ๊ฒฝ๊ณ„์„  ์ตœ์ ํ™” ๋ฌธ์ œ๋ฅผ ๋‹ค๋ฃฌ๋‹ค. ๋Œ€ํ‘œ์ ์ธ ํ˜ผํ•ฉ ์ „๋žต์ธ ์ฐจ๋ณ„ํ™” ์ง€์—ฐ ์ „๋žต์€ ๊ณตํ†ต ๋ฐ˜์ œํ’ˆ์„ ์žฌ๊ณ ๋กœ ๋ณด๊ด€ํ•˜์—ฌ ์‹ค์ œ ์ˆ˜์š”๊ฐ€ ๋ฐœ์ƒํ•˜๋ฉด ๋‚˜๋จธ์ง€ ๊ณต์ •์„ ๊ฑฐ์ณ ๊ณต๊ธ‰ํ•˜๋Š” ๊ฒƒ์„ ์˜๋ฏธํ•œ๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ๋จผ์ € ์ œํ’ˆ๊ณผ ์›๋ฃŒ, ์ƒ์‚ฐ๊ณต์ •์˜ ๋ถ„์„์„ ํ†ตํ•ด ํšจ๊ณผ์ ์ธ ๋ฐ˜์ œํ’ˆ์„ ๋„์ถœํ•˜๊ณ , ์ด๋ฅผ ๋ฐ”ํƒ•์œผ๋กœ ๋ฐ˜์ œํ’ˆ์˜ ์žฌ๊ณ ๊ด€๋ฆฌ ๋ฌธ์ œ๋ฅผ ์ •์˜ํ•˜์—ฌ push-pull ๊ฒฝ๊ณ„์„  ์ตœ์ ํ™”๋ฅผ ๋‹ฌ์„ฑํ•œ๋‹ค. ๊ตฌ์ฒด์ ์œผ๋กœ ๋ฐ˜์ œํ’ˆ ์žฌ๊ณ ๊ด€๋ฆฌ ๋ฌธ์ œ๋Š” ๋ถˆํ™•์ •์  ์ˆ˜์š” ํ•˜์—์„œ ๋ฐ˜์ œํ’ˆ์˜ ๋ชฉํ‘œ ์žฌ๊ณ ๋Ÿ‰๊ณผ ์žฌ๋ณด์ถฉ ์ฃผ๊ธฐ๋ฅผ ๊ตฌํ•˜๋Š” ๊ฒƒ์ด๋‹ค. ์ด๋Š” Joint Replenishment Problem(JRP)์™€ ์œ ์‚ฌํ•˜๋ฉฐ, ๋‘ ๋ฌธ์ œ ๋ชจ๋‘ ์—ฌ๋Ÿฌ ๊ฐœ์˜ ์ฃผ๊ธฐ๋ฅผ ๊ตฌํ•˜๋Š” ๊ฒƒ์ด ๋ฌธ์ œ๋ฅผ ์–ด๋ ต๊ฒŒ ๋งŒ๋“ ๋‹ค. ๋”ฐ๋ผ์„œ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ํœด๋ฆฌ์Šคํ‹ฑ์„ ํ†ตํ•ด ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•œ๋‹ค. NP-hard๋ผ๊ณ  ์•Œ๋ ค์ง„ JRP๋Š” ์ฃผ๊ธฐ๋ฅผ ์ƒ์ˆ˜ ๊ฐ’์œผ๋กœ ๊ณ ์ •ํ•จ์œผ๋กœ์จ ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๋Š”๋ฐ, ๋ณธ ๋ชจํ˜•์—์„œ๋„ ์ด์™€ ์œ ์‚ฌํ•˜๊ฒŒ ์ฃผ๊ธฐ๋ฅผ 2์˜ ์Šน์ˆ˜ ๊ฐ’์œผ๋กœ ๊ณ ์ •ํ•˜๋Š” Power-of-Two policy๋ฅผ ๊ณ ๋ คํ•œ๋‹ค. ์‹คํ—˜์„ ํ†ตํ•ด ๋ฐ˜์ œํ’ˆ ๋„์ž… ์ „ํ›„์™€ ๋น„๊ตํ•˜์—ฌ ๋น„์šฉ์ด ๊ฐ์†Œ๋จ์„ ๋ณด์˜€๋‹ค.1 ์„œ๋ก  1 1.1 ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ์—ฐ๊ตฌ ๋ชฉ์  1 1.2 ๊ธฐ์กด ์—ฐ๊ตฌ 5 1.3 ๋…ผ๋ฌธ ๊ตฌ์„ฑ 8 2 ๊ณตํ†ต ๋ฐ˜์ œํ’ˆ ๋„์ถœ 9 2.1 ํŠน์ˆ˜๊ฐ• ์‚ฐ์—…์˜ ํŠน์ง• 9 2.2 ABC ๋ถ„์„ 11 2.3 ์›๋ฃŒ ๋ถ„์„ 12 2.4 ๊ณต์ • ์กฐํ•ฉ ๋ถ„์„ 12 2.5 ๊ณตํ†ต ๋ฐ˜์ œํ’ˆ ๋„์ถœ ๊ทœ์น™ 14 3 ๋ชจํ˜•ํ™” 19 3.1 ๊ฐœ์š” 19 3.2 ๊ฐ€์ • 19 3.3 ๊ฒฐ์ • ๋ณ€์ˆ˜ 21 3.4 ๋น„์šฉํ•จ์ˆ˜ 21 3.4.1 ๋ฐ˜์ œํ’ˆ ์žฌ๊ณ ๊ฐ€ ์žˆ๋Š” ๊ฒฝ์šฐ 21 3.4.2 ๋ฐ˜์ œํ’ˆ ์žฌ๊ณ ๊ฐ€ ์—†๋Š” ๊ฒฝ์šฐ 22 3.4.3 ์„ ์˜ ์ƒ์‹ค ๋น„์šฉ 23 3.4.4 ์ž”์กด๊ฐ€์น˜ 24 3.5 ๊ฐœ์š” 25 3.6 ํ‘œ๊ธฐ 25 3.7 ๋ชฉ์ ํ•จ์ˆ˜์™€ ๋น„์šฉํ•จ์ˆ˜ 26 3.8 ๋‹จ์ผ ๊ณตํ†ต ๋ฐ˜์ œํ’ˆ ๋ชจํ˜• 28 3.9 ๋ณต์ˆ˜ ๊ณตํ†ต ๋ฐ˜์ œํ’ˆ ๋ชจํ˜• 29 4 ํ•ด๋ฒ• 31 4.1 ๋‹จ์ผ ๊ณตํ†ต ๋ฐ˜์ œํ’ˆ ๋ชจํ˜•์˜ ์ˆ˜๋ฆฌ์  ๊ตฌ์กฐ 31 4.2 ํ•ด๋ฒ• ๊ฐœ์š” 32 4.3 ํœด๋ฆฌ์Šคํ‹ฑ 34 5 ์‹คํ—˜ 37 5.1 ํŒŒ๋ผ๋ฏธํ„ฐ 37 5.2 ๊ฒฐ๊ณผ 38 5.2.1 ์„ ์˜ ์ƒ์‹ค ๋น„์šฉ์— ๋”ฐ๋ฅธ ๊ฒฐ๊ณผ 38 5.2.2 ๊ณ ์ •๋น„์šฉ์— ๋”ฐ๋ฅธ ๊ฒฐ๊ณผ 41 5.2.3 ์„ ์˜ ์ƒ์‹ค ๋น„์šฉ์ด ์—†์„ ๋•Œ์˜ ๊ฒฐ๊ณผ 43 6 ๊ฒฐ๋ก  ๋ฐ ์ถ”ํ›„ ๊ณผ์ œ 44 7 ๋ถ€๋ก 45 ์ฐธ ๊ณ  ๋ฌธ ํ—Œ 47 ์˜๋ฌธ ์ดˆ๋ก 50Maste

    Push-pull: Deterministic search-based DAG scheduling for heterogeneous cluster systems

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    Consider directed acyclic graph ( DAG) scheduling for a large heterogeneous system, which consists of processors with varying processing capabilities and network links with varying bandwidths. The search space of possible task schedules for this problem is immense. One possible approach for this optimization problem, which is NP- hard, is to start with the best task schedule found by a fast deterministic task scheduling algorithm and then iteratively attempt to improve the task schedule by employing a general random guided search method. However, such an approach can lead to extremely long search times, and the solutions found are sometimes not significantly better than those found by the original deterministic task scheduling algorithm. In this paper, we propose an alternative strategy, termed Push- Pull, which starts with the best task schedule found by a fast deterministic task scheduling algorithm and then iteratively attempts to improve the current best solution using a deterministic guided search method. Our simulation results show that given similar runtimes, the Push- Pull algorithm performs well, achieving results similar to or better than all of the other algorithms being compared.X1127sciescopu

    Push-Pull Block Puzzles are Hard

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    This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question [19]. Push-pull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a โ€˜robotโ€™ on a square grid with 1 ร— 1 obstacles. The obstacles cannot be traversed by the robot, but some can be pushed and pulled by the robot into adjacent squares. Thin walls prevent movement between two adjacent squares. This work follows in a long line of algorithms and complexity work on similar problems [3โ€“ 9, 14, 16, 18]. The 2D push-pull block puzzle shows up in the video games Pukoban as well as The Legend of Zelda: A Link to the Past, giving another proof of hardness for the latter [2]. This variant of block-pushing puzzles is of particular interest because of its connections to reversibility, since any action (e.g., push or pull) can be inverted by another valid action (e.g., pull or push)
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