Data Structures

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Parameterized Eulerian Strong Component Arc Deletion Problem on Tournaments

: ์ด ๋…ผ๋ฌธ์€ ๊ทธ๋ž˜ํ”„ ์ด๋ก ์—์„œ ์ค‘์š”ํ•œ ๊ฐœ๋…์ธ ๊ฐ•ํ•˜๊ฒŒ ์—ฐ๊ฒฐ๋œ ๊ทธ๋ž˜ํ”„์™€ ์—์šธ๋Ÿฌ ๊ทธ๋ž˜ํ”„๋ฅผ ๋ฐ”ํƒ•์œผ๋กœ, ํ† ๋„ˆ๋จผํŠธ ๊ทธ๋ž˜ํ”„์—์„œ์˜ Min DESC ๋ฌธ์ œ์— ๋Œ€ํ•ด ๊นŠ๊ฒŒ ๋ถ„์„ํ•œ๋‹ค. Min DESC ๋ฌธ์ œ๋Š” ์ฃผ์–ด์ง„ ์œ ํ–ฅ ๊ทธ๋ž˜ํ”„ D ์—์„œ ์ตœ์†Œ ๊ฐ„์„  ์ง‘ํ•ฉ์„ ์ œ๊ฑฐํ•˜์—ฌ ๋ชจ๋“  ๊ฐ•ํ•œ ์„ฑ๋ถ„์ด ์—์šธ๋Ÿฌ ๊ทธ๋ž˜ํ”„๊ฐ€ ๋˜๋„๋ก ํ•˜๋Š” ๋ฌธ์ œ์ด๋‹ค. 1. ๊ฐœ๋… ์ •์˜์™€ ๋ฐฐ๊ฒฝ ๋…ผ๋ฌธ์€ ๋จผ์ € ๊ฐ•ํ•˜๊ฒŒ ์—ฐ๊ฒฐ๋œ ๊ทธ๋ž˜ํ”„์™€ ์—์šธ๋Ÿฌ ๊ทธ๋ž˜ํ”„์— ๋Œ€ํ•œ ๊ธฐ๋ณธ์ ์ธ ์ •์˜๋ฅผ ์†Œ๊ฐœํ•œ๋‹ค. ํŠนํžˆ, ๊ฐ•ํ•œ ์„ฑ๋ถ„๊ณผ DESC ์„ธํŠธ์˜ ์ •์˜๋ฅผ ํ†ตํ•ด Min DESC ๋ฌธ์ œ๋ฅผ ๋ช…ํ™•ํžˆ ํ•œ๋‹ค. ์ด๋Š” D ์—์„œ ๊ฐ„์„  ์ง‘ํ•ฉ์„ ์ œ๊ฑฐํ•˜์—ฌ ๋ชจ๋“  ๊ฐ•ํ•œ

Computational Complexity Computer Science Data Structures
A note on the generalized min-sum set cover problem

A note on the generalized min-sum set cover problem

๋งค๋ ฅ์ ์ธ ํ•œ๊ธ€ ์ œ๋ชฉ: ์ผ๋ฐ˜ํ™”๋œ ์ตœ์†Œ ํ•ฉ ์ง‘ํ•ฉ ์ปค๋ฒ„ ๋ฌธ์ œ์— ๋Œ€ํ•œ ๊ฐœ์„ ๋œ ์•Œ๊ณ ๋ฆฌ์ฆ˜ ์ดˆ๋ก ์ „์ฒด ๋ฒˆ์—ญ ๋ฐ ์ •๋ฆฌ: ์ด ๋…ผ๋ฌธ์—์„œ๋Š” ์ผ๋ฐ˜ํ™”๋œ ์ตœ์†Œ ํ•ฉ ์ง‘ํ•ฉ ์ปค๋ฒ„ ๋ฌธ์ œ๋ฅผ ๋‹ค๋ฃจ๋ฉฐ, ์ด ๋ฌธ์ œ๋Š” Feige, Lovรกsz, Tetali์™€ Hassin, Levin์ด ๊ฐ๊ฐ ์†Œ๊ฐœํ•œ ์ตœ์†Œ ํ•ฉ ์ง‘ํ•ฉ ์ปค๋ฒ„ ๋ฌธ์ œ์™€ ์ตœ์†Œ ์ง€์—ฐ ์ง‘ํ•ฉ ์ปค๋ฒ„ ๋ฌธ์ œ์˜ ์ผ๋ฐ˜ํ™”์ž…๋‹ˆ๋‹ค. Azar, Gamzu, Yin์€ O(log r) ๊ทผ์‚ฌ ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์ œ์‹œํ–ˆ์œผ๋ฉฐ, Bansal, Gupta, Krishnaswamy๋Š” ์ด๋ฅผ ๊ฐœ์„ ํ•˜์—ฌ 485.1์˜ ์„ฑ๋Šฅ ๋ณด์žฅ์„ ๋‹ฌ์„ฑํ–ˆ์Šต๋‹ˆ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” Skutella

Data Structures Computer Science
A deterministic algorithm for fitting a step function to a weighted point-set

A deterministic algorithm for fitting a step function to a weighted point-set

: ๋ณธ ๋…ผ๋ฌธ์€ k๋‹จ๊ณ„ ํ•จ์ˆ˜๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ๊ฐ€์ค‘๋œ ์  ์ง‘ํ•ฉ์„ ๊ทผ์‚ฌํ•˜๋Š” ๋ฌธ์ œ์— ๋Œ€ํ•œ ์ƒˆ๋กœ์šด ์ ‘๊ทผ ๋ฐฉ์‹์„ ์ œ์•ˆํ•˜๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. ์ด ๋ฌธ์ œ๋Š” ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค ์‘์šฉ ํ”„๋กœ๊ทธ๋žจ์—์„œ ํšจ์œจ์ ์ธ ๋ฐ์ดํ„ฐ ์ €์žฅ ๋ฐ ์ฟผ๋ฆฌ ์ฒ˜๋ฆฌ ์†๋„ ํ–ฅ์ƒ์„ ์œ„ํ•ด ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•ฉ๋‹ˆ๋‹ค. 1. k๋‹จ๊ณ„ ํ•จ์ˆ˜์™€ ์ค‘๋Ÿ‰์ ์˜ ์ •์˜ k๋‹จ๊ณ„ ํ•จ์ˆ˜๋Š” ์‹ค์ˆ˜ ์‹œํ€€์Šค๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ๊ฐ ๊ตฌ๊ฐ„์— ์ƒ์ˆ˜ ๊ฐ’์„ ๊ฐ€์ง€๋Š” ํ•จ์ˆ˜์ž…๋‹ˆ๋‹ค. ์ค‘๋Ÿ‰์ ์€ (x, y, w)๋กœ ํ‘œํ˜„๋˜๋ฉฐ, ์—ฌ๊ธฐ์„œ x์™€ y๋Š” ์ ์˜ ์ขŒํ‘œ์ด๊ณ , w๋Š” ํ•ด๋‹น ์ ์˜ ๋ฌด๊ฒŒ๋ฅผ ๋‚˜ํƒ€๋ƒ…๋‹ˆ๋‹ค. 2. ๊ทผ์‚ฌ ๋ฌธ์ œ ์ฃผ์–ด์ง„ ๊ฐ€์ค‘๋œ ์  ์ง‘ํ•ฉ P์— ๋Œ€ํ•ด k๋‹จ๊ณ„ ํ•จ์ˆ˜ f๋ฅผ ์ฐพ์•„์„œ P์™€

Computational Geometry Computer Science Data Structures
Sorting Algorithms with Restrictions

Sorting Algorithms with Restrictions

์ด ๋…ผ๋ฌธ์€ ์ •๋ ฌ ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ์ œํ•œ ์กฐ๊ฑด๊ณผ ๊ทธ์— ๋”ฐ๋ฅธ ๋ณต์žก๋„๋ฅผ ๊นŠ๊ฒŒ ํƒ๊ตฌํ•˜๋ฉฐ, ํŠนํžˆ $k$ ์ •๋ ฌ ๋ฐฉ์‹๊ณผ ๋ณ‘๋ ฌ ์ •๋ ฌ ๋ฐฉ์‹์„ ์ค‘์ ์ ์œผ๋กœ ๋‹ค๋ฃฌ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ์ „ํ†ต์ ์ธ ์ •๋ ฌ ์•Œ๊ณ ๋ฆฌ์ฆ˜์—์„œ ๋ฒ—์–ด๋‚˜ ์ƒˆ๋กœ์šด ํ™˜๊ฒฝ๊ณผ ์š”๊ตฌ ์‚ฌํ•ญ์— ๋งž์ถ˜ ์ •๋ ฌ ๋ฐฉ๋ฒ•๋ก ์„ ์ œ์‹œํ•œ๋‹ค. 1. ์„œ๋ก  ์„œ๋ก ์—์„œ๋Š” ์ •๋ ฌ์ด ๊ฐ€์žฅ ๋„๋ฆฌ ์‚ฌ์šฉ๋˜๊ณ  ์‹ฌ๋„ ์žˆ๊ฒŒ ์—ฐ๊ตฌ๋œ ๋ฌธ์ œ ์ค‘ ํ•˜๋‚˜๋ผ๋Š” ์ ์„ ๊ฐ•์กฐํ•˜๋ฉฐ, ์ „ํ†ต์ ์ธ ๊ฐ€์ •์—์„œ ๋ฒ—์–ด๋‚˜ ์ƒˆ๋กœ์šด ํ”„๋กœ์„ธ์„œ์™€ ๋ฐ์ดํ„ฐ ์ŠคํŠธ๋ฆผ์˜ ๋“ฑ์žฅ์œผ๋กœ ์ธํ•ด ๋ณ€ํ™”ํ•˜๋Š” ์ •๋ ฌ ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ๋ชจ์Šต์— ๋Œ€ํ•ด ๋…ผํ•œ๋‹ค. ์ด๋Š” ๊ธฐ์กด์˜ ์ •๋ ฌ ์•Œ๊ณ ๋ฆฌ์ฆ˜์ด ๋‹จ์ˆœํžˆ ๋‘ ์ˆซ์ž๋ฅผ ๋น„๊ตํ•˜์—ฌ ์ •๋ ฌํ•˜๋Š” ๋ฐฉ์‹์—์„œ ๋ฒ—์–ด

Computer Science Data Structures

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