HK ZO final (2007. 6. 15) - &h ú: ( ) / 100

H K Z O final

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Ò_:—¸ŽHõ&ñ`¦&ñSX‰y ]jr½+É כ .

1. P6= NP€, #Q*‹ôDz >0\ @/K"f•¸ BjàÔaË:k-G'p' _

(2−²)-HKZO“Ér Ô¦0px.

2. 6£§õ °ú “Érgknap ëH]j\¦ÒqtyŒ•. min c^Tx

s.t x∈Q d^Tx≤, B, x∈ {0,1}ⁿ.

where, Q, poly-separable 0−1 polytope, c, d∈ Zⁿ₊, and B ∈Z+.

(1) s ëH]j_ þj&h3lq&h†<Êú °úכ`¦ OPT, c\¦ ˆcj = b_²C/n^cj c–Ð Û¼H{9#Œ %3“Ér ëH]j_ þj&hK\¦x,ˆ þj&h3lq&h

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Êú°úכ`¦OPTs[“¦Ùþ¡`¦M: 6£§`¦ 7£x"î. c^Tx < OP Tˆ +²C, OP T >[ bn

²c ⇒OP T > C, OP T[ ≤ bn

²c ⇒OP T <(1 +²)C.

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(2) gkanps FPTAS\¦ |9 €9כ¹Øæìr›¸|“Ér poly(n, cmax,hdmaxi) rçߖ îߖ\ Û¦oH כ e”`¦ s6 x

#Œ, poly(n,hcmaxi, dmax) rçߖ îߖ\ Û¦oH כ •¸ gkanp_FPTAS\¦|9€9כ¹Øæìr›¸|e”`¦ 7£x"î.

3. 6£§õ °ú “Ér Max-SatëH]j_ randomized ·ú˜“¦o1pu`¦ Ò

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tyŒ•:yŒ•Ãº1lqwn&hܼ–Ð ¹₂ SX‰Ò¦–ÐTrue ÷&•¸2Ÿ¤

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o°úכ`¦Òqt$íôÇ.

(1) yŒ•]X_o'XO_>hú2>h s©œs€3/4-HK Z

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s ÷&Hכ `¦ 7£x"î.

(2) derandomized·ú˜“¦o1pu`¦]jr“¦ s\¦ 7£x"î.

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4. 6£§õ °ú “ÉrSet CoverëH]j\¦ÒqtyŒ•.

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]:Ä»ôÇ|9½+ËU, |U|=n. U_ÂÒìr|9½+Ë_c+t7˜‚S = {S1, . . . , Sm},c:S −→Q+.

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¦†\B:½+ˀU ÷&HS_þj™èq6 xÂÒìr c+t7˜‚. (1)6£§sf-H·ú˜“¦o1pue”`¦ 7£x"î.

LP-rounding algorithm 1. ‚+þA¢-aoëH]j_þj&hK\¦½¨ôÇ;

2. xS ≥_f¹“S\¦—¸¿º “¦Ér.

(2)6£§sf-H·ú˜“¦o1pue”`¦ 7£x"î. Set Cover xjS-3‘×7FD9 N±Ó”§hžæ¸

1. x←0, y←0;

2. —¸ŽH"鶙è &!Q|¨cM: t6£§`¦ìøÍ4Ÿ¤ôÇ:

f”&!Q÷&t·ú§“Ére”_"鶙èe\¦‚×þ˜ôÇ; 1

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x ñ–Ðëߖ7á¤÷&HŠ©œ@/ ]j€•d”sÒqtU´M: t y_e\¦ 7£xr†;

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x ñ–Ðëߖ7á¤÷&H]j€•d”_|9½+Ë[þt`¦

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¸¿º &!Q\V,“¦ s\ xS\¦\OX<sàÔôÇ; s

M: Dh\v> &!Q÷&H"鶙è[þt`¦\OX<sàÔôÇ. 3. |9½+Ë&!Qx\¦ ئ§4ôÇ.

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