Paper Abstract and Keywords |
Presentation |
2011-03-09 14:10
Constant-time approximation algorithms for the knapsack problem Hiro Ito, Susumu Kiyoshima, Yuichi Yoshida (Kyoto Univ.) COMP2010-51 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
In this paper, we give constant-time approximation algorithms
for the knapsack problem.
A randomized algorithm is called an $\epsilon$-approximation algorithm
if it outputs the optimal value with an additive error $\epsilon$ with probability at least $2/3$. Here, the total value of items is normalized to $1$. By using weighted sampling, with which we can sample items with
probability proportional to their values, we give an $\epsilon$-approximation algorithm for the knapsack problem, which runs in $O(\epsilon^{-4}\log \epsilon^{-1})$ time. We also give an $\epsilon$-approximation algorithm for the subset sum problem, which runs in $O(\epsilon^{-2})$ time. We also show that $\Omega(n)$ samplings are necessary if uniform sampling, which selects every item with uniform probability, is used. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
knapsack problem / subset sum problem / constant-time approximation algorithm / / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 110, no. 464, COMP2010-51, pp. 29-36, March 2011. |
Paper # |
COMP2010-51 |
Date of Issue |
2011-03-02 (COMP) |
ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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COMP2010-51 |
Conference Information |
Committee |
COMP |
Conference Date |
2011-03-09 - 2011-03-09 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Chuo Univ. |
Topics (in Japanese) |
(See Japanese page) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2011-03-COMP |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Constant-time approximation algorithms for the knapsack problem |
Sub Title (in English) |
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knapsack problem |
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subset sum problem |
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constant-time approximation algorithm |
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1st Author's Name |
Hiro Ito |
1st Author's Affiliation |
Kyoto University (Kyoto Univ.) |
2nd Author's Name |
Susumu Kiyoshima |
2nd Author's Affiliation |
Kyoto University (Kyoto Univ.) |
3rd Author's Name |
Yuichi Yoshida |
3rd Author's Affiliation |
Kyoto University (Kyoto Univ.) |
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Speaker |
Author-2 |
Date Time |
2011-03-09 14:10:00 |
Presentation Time |
35 minutes |
Registration for |
COMP |
Paper # |
COMP2010-51 |
Volume (vol) |
vol.110 |
Number (no) |
no.464 |
Page |
pp.29-36 |
#Pages |
8 |
Date of Issue |
2011-03-02 (COMP) |
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