Paper Abstract and Keywords |
Presentation |
2011-06-30 14:40
On the Constant Depth Circuit Complexity of Subgraph Isomorphism on Random Graphs Koutarou Nakagawa (Tokyo Inst. of Tech.) COMP2011-20 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
The AC$^0$ circuit complexity of $k$-clique on random graphs is already known. Rossman established the lower bound $n^{\omega(k/4)}$ in 2008, and Amano establishd the upper bound $n^{O(k/4)+o(1)}$ in 2009. But complexity of subgraph isomorphism is still unknown.
These results, for compute complexity of $k$-clique problem, are can applcate to subgraph isomorphism.
So by the new function $c(H)$ and $\tilde c(H)$, we can represent the Rossman's result is $n^{c(H)}$ lower bound and Amano's result is $n^{\tilde c(H)}$ upper bound of subgraph isomorphism. But $c(H)$ and $\tilde c(H)$ are not so simple.
In this paper, we prove that these bounds are not tight, namely, gap between $c(H)$ and $\tilde c(H)$ is large by showing that a family of graph that elements have constant $c(H)$ and proportion to the size $tilda c(H)$.
This means that, the complexity of this problem is still unknown, and $c(H)$ or $\tilde c(H)$ to be room for implovement. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Circuit complexity / constant depth circuits / subgraph isomorphism / lower bounds / upper bounds / / / |
Reference Info. |
IEICE Tech. Rep., vol. 111, no. 113, COMP2011-20, pp. 33-37, June 2011. |
Paper # |
COMP2011-20 |
Date of Issue |
2011-06-23 (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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COMP2011-20 |
Conference Information |
Committee |
COMP |
Conference Date |
2011-06-30 - 2011-06-30 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Hiroshima Univ. |
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(See Japanese page) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2011-06-COMP |
Language |
English (Japanese title is available) |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
On the Constant Depth Circuit Complexity of Subgraph Isomorphism on Random Graphs |
Sub Title (in English) |
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Circuit complexity |
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constant depth circuits |
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subgraph isomorphism |
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lower bounds |
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upper bounds |
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1st Author's Name |
Koutarou Nakagawa |
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Tokyo Institute of Technology (Tokyo Inst. of Tech.) |
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Speaker |
Author-1 |
Date Time |
2011-06-30 14:40:00 |
Presentation Time |
35 minutes |
Registration for |
COMP |
Paper # |
COMP2011-20 |
Volume (vol) |
vol.111 |
Number (no) |
no.113 |
Page |
pp.33-37 |
#Pages |
5 |
Date of Issue |
2011-06-23 (COMP) |
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