岩間研究室 発表論文
2004年度
[ 論文誌 ]
- id=2004-02
- A. Uejima, H. Ito, and T. Tsukiji,
- ``$\overline{C_7}$-coloring problem'',
-
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.E87-A, no.5, pp.1243--1250, May 2004.
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>> Abstract
- id=2004-04
- K. Iwama, and K. Yonezawa,
- ``The Orthogonal CNN Problem'',
-
Information Processing Letters, vol.90, no.3, pp.115--120, May 2004.
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>> Abstract
- id=2004-05
- K. Iwama, and K. Yonezawa,
- ``The Axis-bound CNN Problem'',
-
IEICE Transactions on Fundamentals, vol.87E-A, no.5, pp.1235--1242, May 2004.
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>> Abstract
- id=2004-14
- T. Horiyama, and T. Ibaraki,
- ``Reasoning with Ordered Binary Decision Diagrams'',
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Discrete Applied Mathematics, vol.142/1-3, pp.151--163, Aug. 2004.
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>> Abstract
- id=2004-19
- M. Halld\'orsson, K. Iwama, S. Miyazaki, and H. Yanagisawa,
- ``Randomized Approximation of the Stable Marriage Problem'',
-
Theoretical Computer Science, vol.325, no.3, pp.439--465, Oct. 2004.
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>> Abstract
- id=2004-23
- H. Miwa, and H. Ito,
- ``NA-Edge-Connectivity Augmentation Problems by Adding Edges'',
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Journal of the Operations Reserch Society of Japan, vol.47, no.4, pp.224--243, Dec. 2004.
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>> Abstract
- id=2004-24
- K. Iwama, A. Kawachi, and S. Yamashita,
- ``Quantum Sampling for Balanced Allocations'',
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IEICE Trans. Inf. \& Syst., Special Issue on Foundations of Computer Science, vol.E88-D, no.1, pp.39--46, Jan. 2005.
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>> Abstract
- id=2004-25
- K. Iwama, and A. Kawachi,
- ``Compact Routing with Stretch Factor of Less Than Three'',
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IEICE Trans. Inf. \& Syst., Special Issue on Foundations of Computer Science, vol.E88-D, no.1, pp.47--52, Jan. 2005.
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>> Abstract
- id=2004-31
- H. Fujiwara, and K. Iwama,
- ``Average-Case Competitive Analyses for Ski-Rental Problems'',
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Algorithmica, vol.42, no.1, pp.95--107, Mar. 2005.
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>> Abstract
- id=2004-34
- H. Ito, K. Iwama, Y. Okabe, and T. Yoshihiro,
- ``Single-Backup-Table Schemes for Shortest-Path Routing'',
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Theoretical Computer Science, vol.333, no.3, pp.347--353, Mar. 2005.
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>> Abstract
[ 国際会議 ]
- id=2004-03
- A. Uejima, and H. Ito,
- ``Subdivision of the Hierarchy of H-Colorable Graph Classes by Circulant Graphs'',
-
Workshop on Graphs and Combinatorial Optimization (CTW04), pp.232--236, May 2004.
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>> Abstract
- id=2004-07
- K. Iwama, S. Miyazaki, and K. Okamoto,
- ``A $(2 - c \log N / N)$-Approximation Algorithm for the Stable Marriage Problem'',
-
Proc. the 9th Scandinavian Workshop on Algorithm Theory (SWAT 2004), LNCS 3111, pp.349--361, Jul. 2004.
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>> Abstract
- id=2004-08
- K. Iwama,
- ``Automated competitive analysis of online algorithms'',
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Workshop on On-Line Algorithms (OLA 2004), Jul. 2004.
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>> Abstract
- id=2004-15
- T. Imamura, K. Iwama, and T. Tsukiji,
- ``Approximated Vertex Cover for Graphs with Perfect Matchings'',
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Proc. 10th Annual International Conference (COCOON 2004), pp.132--142, Aug. 2004.
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>> Abstract
- id=2004-16
- H. Ito, K. Iwama, and T. Tamura,
- ``Imperfectness of Data for STS-Based Physical Mapping'',
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Proc. the 3rd IFIP International Conference on Theoretical Computer Science (TCS2004), pp.279--292, Aug. 2004.
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>> Abstract
- id=2004-17
- A. Kawachi, H. Kobayashi, T. Koshiba, and Rudy Raymond H.P.,
- ``Universal Test for Quantum One-Way Permutations'',
-
Proc. the 29th International Symposium on Mathematical Foundations of Computer Science (MFCS 2004), LNCS 3153, pp.839--850, Aug. 2004.
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>> Abstract
- id=2004-20
- H. Ito,
- ``Three equivalent partial orders on graphs with real edge-weights drawn on a convex polygon'',
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Proc. the Japan Conference on Discrete and Computational Geometry (JCDCG2004), LNCS 3742, pp.123--130, Oct. 2004.
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>> Abstract
- id=2004-21
- N. Doi, T. Horiyama, M. Nakanishi, and S. Kimura,
- ``An Optimization Method in Floating-point to Fixed-point Conversion using Positive and Negative Error Analysis and Sharing of Operations'',
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Proc. the 12th Workshop on Synthesis And System Integration of Mixed Information Technologies (SASIMI 2004), pp.466--471, Oct. 2004.
- id=2004-22
- K. Iwama, and A. Kawachi,
- ``Approximated Two Choices in Randomized Load Balancing'',
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Proc. the 15th Annual International Symposium on Algorithms and Computation (ISAAC 2004), LNCS 3341, pp.545--557, Dec. 2004.
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>> Abstract
- id=2004-26
- T. Imamura, and K. Iwama,
- ``Approximating Vertex Cover on Dense Graphs'',
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Proc. 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), pp., Jan. 2005.
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>> Abstract
- id=2004-28
- H. Fujiwara, and K. Iwama,
- ``Average-Case Competitive Analyses for Ski-Rental Problems'',
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Dagstuhl Seminar 05031 (Algorithms for Optimization with Incomplete Information), Jan. 2005.
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>> Abstract
- id=2004-29
- K. Iwama, A. Kawachi, Rudy Raymond H.P., and S. Yamashita,
- ``Robust Quantum Algorithms for Oracle Indentification'',
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Proc. 8th workshop on Quantum Information Processing (QIP 2005), Jan. 2005.
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>> Abstract
[ 国内発表 ]
- id=2004-01
- 岡本和也, 宮崎修一, 岩間一雄,
- ``局所探索法による安定結婚問題の近似'',
- 電子情報通信学会 コンピュテーション研究会, 信学技報, vol.104, no.16, COMP2004-8, pp.53--60, 2004年 4月.
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>> Abstract
- id=2004-06
- 中塚裕之, 堀山貴史, 岩間一雄,
- ``逆算法に基づく詰将棋の列挙'',
- 電子情報通信学会 コンピュテーション研究会, 信学技報, vol.104, COMP2004-20, pp.11--18, 2004年 6月.
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>> Abstract
- id=2004-09
- 河内亮周, 山下茂, 岩間一雄,
- ``オラクル同定問題に対する頑健な量子アルゴリズム'',
- 情報処理学会 アルゴリズム研究会, 情処研報, 2004-AL-96, 2004-AL-96, pp.1--8, 2004年 7月.
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>> Abstract
- id=2004-10
- J. Kawahara, T. Horiyama, K. Iwama,
- ``Automated Proof of Competitive Ratios for Online Problems'',
- 夏のLAシンポジウム, pp.22.1--22.4, 2004年 7月.
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>> Abstract
- id=2004-11
- A. Kawachi, H. Kobayashi, T. Koshiba, and Rudy Raymond H.P.,
- ``Universal Test for Quantum One-Way Permutations'',
- 夏のLAシンポジウム, pp.23.1--23.12, Jul. 2004.
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>> Abstract
- id=2004-12
- X. Han, K. Iwama, and G. Zhang,
- ``On-line Removable Square Packing'',
- 夏のLAシンポジウム, Jul. 2004.
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>> Abstract
- id=2004-13
- 土井伸洋, 中西正樹, 堀山貴史, 木村晋二,
- ``浮動小数点演算での誤差の増減を考慮した変数のビット長最適化'',
- 情報処理学会 DA シンポジウム 2004 論文集, B2-2, pp.85--90, 2004年 7月.
- id=2004-18
- 土井伸洋, 堀山貴史, 中西正樹, 木村晋二,
- ``負方向への誤差を考慮した高位合成向けビット長最適化手法'',
- 電子情報通信学会ソサエティ大会講演論文集, AS-3-1, 2004年 9月.
- id=2004-27
- 田村武幸, 伊藤大雄, 岩間一雄,
- ``遺伝的な距離に基づいた家系図推定問題'',
- 電子情報通信学会 コンピュテーション研究会, 信学技報, vol.104, no.642, pp.33--39, 2005年 1月.
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>> Abstract
- id=2004-30
- Y. Hanatani, T. Horiyama, and K. Iwama,
- ``Haj\'os Calculus on Planar Graphs'',
- 冬のLAシンポジウム, pp.3.1--3.4, Feb. 2005.
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>> Abstract
- id=2004-33
- 土井伸洋, 堀山貴史, 中西正樹, 木村晋二,
- ``非線形計画法と整数解の探索に基づく高位合成向けビット長最適化'',
- 情報処理学会, システムLSI設計技術研究会, 2005-SLDM-119(23), pp.133--138, 2005年 3月.
[ 解説 ]
- id=2004-32
- 宮崎修一,
- ``安定結婚問題'',
- 電子情報通信学会誌, vol.88, no.3, pp.195--199, 2005年 3月.
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>> Abstract
Abstract
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id=2004-01
- 安定結婚問題の例題では、各個人の希望リストは異性全員を含み、
完全に順位付けされている必要がある。しかし、実世界での応用を考えると、
ペアになりたくない相手は希望リストに書かない不完全リストや、
好みが同じ程度の人は優劣をつけなくて良い同順位リストという
2つの自然な拡張が考えられる。どちらか一方の拡張のみを許した問題は
多項式時間で解くことができるが、
両方の拡張を許した場合、最大サイズの安定マッチングを見つける問題は
NP困難になることが知られている。
任意の2つの安定マッチングのサイズは最大でも2倍しか異ならないということは
簡単にわかるため、近似度が2の近似アルゴリズムは自明である。
2よりも良い近似度を実現する近似アルゴリズムを与える結果は
いくつか知られているが、それらは、
例えば同順位の長さや出現数などの制限を加えられた下でのものだけである。
現在まで一般的な入力に対し、
近似度が2未満となる近似アルゴリズムは知られていない。
本論文では、一般的な例題に対し、近似度が2未満となる非自明な結果を
初めて示した。我々のアルゴリズムの近似度は$2-c\frac{\log N}{N}$である。
(ここで、$c$は任意の正定数で、$N$は入力中の男性の数である。)
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id=2004-02
- $H$-coloring problem is a coloring problem with restrictions such
that some pairs of colors cannot be used for adjacent vertices, where
$H$ is a graph representing the restrictions of colors. We deal with the
case that $H$ is the complement graph $\overline{C_{2p+1}}$ of a cycle
of odd order $2p+1$. This paper presents the following results: (1)
chordal graphs and internally maximal planar graphs are
$\overline{C_{2p+1}}$-colorable if and only if they are $p$-colorable
($p \geq 2$), (2) $\overline{C_7}$-coloring problem on planar graphs is
NP-complete, and (3) there exists a class that includes infinitely many
$\overline{C_7}$-colorable but non-3-colorable planar graphs.
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id=2004-03
- For any integer $p \geq 2$, $p$-colorable graphs are
$\overline{C_{2p+1}}$-colorable and $\overline{C_{2p+1}}$-colorable
graphs are $p+1$-colorable, where $\overline{C_{2p+1}}$ is the
complement graph of a cycle of order $2p+1$. The converse statements are
however incorrect. This paper presents that the above inclusion can be
subdivided by a subset of circulant graphs $H(n, k)~(n, k \in
\mbox{\boldmath $N$},~k \leq \lfloor n/2 \rfloor)$. The subdivided
hierarchy of inclusion contains the well-known inclusion of
$C_{2p+1}$-colorable graphs. Moreover, we prove some NP-complete
problems for planar $H(n, k)$-colorings, including the
$\overline{C_5}$-coloring.
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id=2004-04
- The online CNN Problem had no known competitive
algorithms for a long time. Sitters, Stougie and
de Paepe showed that there exists a competitive online algorithm
for this problem. However, both their algorithm and analysis are
quite complicated, and above all, their upper bound for
the competitive ratio is $10^5$.
In this paper, we examine why this problem seems so difficult.
To this end we introduce a nontrivial restriction, orthogonality,
against this problem and show that it decreases the competitive ratio
dramatically, down to at most 9.
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id=2004-05
- In the CNN problem, a ``scene'' appears on the
two-dimensional plane, at different positions sequentially, and a
``camera crew'' has to shoot the scene whenever it appears.
If a scene appears at some position, the camera crew does not have to
move to the position exactly, but has only to move to a point that
lies in the same horizontal or vertical line with the scene.
Namely it is enough to move either to the same row or to the same column.
The goal is to minimize the total moving distance of the camera crew.
This problem has been quite popular in the last decade but it
is still open whether or not there is a competitive algorithm,
i.e., an algorithm with competitive ratio bounded by a constant.
In this paper we study this problem under a natural restriction
that the server can move only along the $X$-axis
and the $Y$-axis. It is shown that there exists a competitive
algorithm for this restricted version, namely
there is an online algorithm for this ``axis-bound CNN''
with competitive ratio $9.0$.
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id=2004-06
- 近年の計算機の高速化や大容量化、
洗練されたアルゴリズム設計法の発展により、
与えられた条件を満たす解を1つだけでなくすべて列挙することが、
実用上要請されるようになってきている。
本研究では、逆算法による詰将棋の列挙アルゴリズムを提案する。
従来手法では、詰将棋となる可能性のある局面を数え挙げ、
これを順に詰将棋解答プログラムに解かせて
それぞれが詰将棋として成立していることを確認しているため、
実行時間が長くなりがちである。
本手法では、逆算法により詰め手数の少ないものから順に詰将棋を
列挙することで、詰将棋解答プログラムを用いることなく、
与えられた条件下で可能な詰将棋を高速に列挙することができる。
また、提案アルゴリズムをC言語で実装し、
桂図式等の複数の条件において列挙を行う。
生成可能なものをすべて数え挙げられるため、
例えば桂図式は最長手数が9手である等、
各図式の最長手数を証明したことになる。
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id=2004-07
- We propose an approximation algorithm for the problem of finding a
maximum stable matching when both ties and unacceptable partners are
allowed in preference lists. Our algorithm achieves the approximation
ratio $2-c\frac{\log N}{N}$ for an arbitrarily positive constant $c$,
where $N$ denotes the number of men in an input. This improves the
trivial approximation ratio of two.
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id=2004-08
- The main objective of this paper is to present a rather general
framework for automated competitive analysis, i.e., for using
computers to prove a competitive ratio of online algorithms. As an
example, we use the Exchangeable Online Knapsack problem and prove an
upper bound of 1.3334 for its competitive ratio using our system.
There are two features: (i) Our system automatically generates
different "states" of the game, the entire size of which is usually
much larger than the size of the algorithm description. (ii) For
claiming a concrete value for the competitive ratio, our system can
use formula expression or does not have to depend on numerical
analysis. For this purpose our system includes Mathematica as a part
of the system.
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id=2004-09
- オラクル同定問題とは
$n$ビット入力$1$ビット出力のオラクルの集合$S=\{f_1,...,f_M\}$と
$S$に属する未知のオラクル$f_i$が与えられたとき,
未知のオラクル$f_i$を$S$の中から同定する問題であり,
数多くの問題の一般化になっている.本稿では,
与えられた未知のオラクルクエリーの結果が
正しい値と誤った値が重ね合わせ状態として出力される場合の
オラクル同定問題(但し,誤った計算結果が得られる確率は
$1/2$より小さい定数確率,例えば$1/10$以下とする.)に対して以下を示す.
(i)~与えられたオラクル集合のサイズが$N=2^n$の場合(すなわち$M=N$.),
エラー付きオラクル同定問題をクエリー回数$O(\sqrt{N})$で少なくとも
定数確率で解く量子アルゴリズムが構成できる.
(ii)~与えられたオラクル集合のサイズが$N$の場合,
各$x\in\{0,1\}^n$で$f_i(x)=1$を満たす$i$の数に関するパラメータ$K$に関して
ある条件を満たすとき,エラー付きオラクル同定問題を
クエリー回数$O(\sqrt{N/K})$で
少なくとも定数確率で解く量子アルゴリズムが構成できる.
-
id=2004-10
- 種々のオンライン問題では、オンラインアルゴリズムを設計し、
競合比を計算するが、しばしば場合分けが膨大な数に及ぶことがある。
今回はそのような問題の代表としてオンラインナップザック問題を考える。
オンラインナップザック問題はプレイヤはアイテムが一つずつ順番に与えられ、
そのたびにそのアイテムをナップザックの中に入れるか捨てるかを決める
オンライン問題である。
この問題の競合比上限を証明するとき、
アイテムのサイズによる場合分けが20種類以上にも及ぶことが分かった[1]。
そこで、この場合分けを計算機を用いて自動的に生成し、競合比の証明を行う。
本稿では交換可能オンラインナップザック問題(EOK)での$k=2$の場合の上限が
1.3334であることを計算機を用いて証明を行った。
-
id=2004-11
- The next bit test was introduced by Blum and Micali
and proved by Yao to be a universal test
for cryptographic pseudorandom generators. On the other hand,
no universal test for the cryptographic one-wayness of
functions (or permutations) is
known, though the existence of cryptographic pseudorandom generators
is equivalent to that of cryptographic one-way functions.
In the quantum computation model, Kashefi, Nishimura and Vedral
gave a sufficient condition of (cryptographic)
quantum one-way permutations and conjectured that the condition
would be necessary. In this paper, we relax their sufficient condition
and give a new condition that is necessary and sufficient for
quantum one-way permutations. Our condition can be regarded
as a universal test for quantum one-way permutations, since our
condition is described as a collection of stepwise tests similar to
the next bit test for pseudorandom generators.
-
id=2004-12
- In this paper, we consider an on-line square packing problem:
Given a list of squares with side length of at most 1, we are
asked to pack a subset of them, in an on-line manner and
without any overlap, into a unit square bin so that the
packed area (the total area of squares packed) is as large as
possible. We assume that removal is allowed. It means that a
packed square can be removed from the square bin. However,
once a square is rejected or removed it will never been
considered again. We first show a lower bound of 2.618 for
any on-line algorithm. Then we propose an on-line algorithm
based on partitioning the square bin into bricks and show a
competitive ratio of 3. As a byproduct it is proved that any
list of squares with total area no more than 1/3 can be
on-line packed in a unit square, which improves the previous
best known result by Januszewski and Lassak.
-
id=2004-14
- We consider problems of reasoning with a knowledge-base, which is
represented by an ordered binary decision diagram (OBDD), for two
cases of general and Horn knowledge-bases. Our main results say
that both finding a model of a knowledge-base and deducing from a
knowledge-base can be done in linear time for a general knowledge-base,
but that abduction is NP-complete even for a Horn knowledge-base.
Then, we consider abduction when its assumption set consists
of all propositional literals (i.e., an answer for a given query
is allowed to include any positive literals), and show that it can
be done in polynomial time if the knowledge-base is Horn, while it
remains NP-complete for the general case. Some other solvable cases
are also discussed.
-
id=2004-15
- Chen and Kanj considered the Vertex Cover problem for graphs
with perfect matchings (VC-PM). They showed that: (i) There
is a reduction from general Vertex Cover to VC-PM, which
guarantees that if one can achieve an approximation factor of
less than two for VC-PM, then one can do so for general
Vertex Cover as well. (ii) There is an algorithm for VC-PM
whose approximation factor is given as $1.069 + 0.069d$ where $d$
is the average degree of the given graph. In this paper we
improve (ii). Namely we give a new VC-PM algorithm which
greatly outperforms the above one and its approximation
factor is roughly $2 - \frac{6.74}{d+6.28}$. Our algorithm
also works for graphs with ``large'' matchings although its
approximation factor is degenerated.
-
id=2004-16
- In the STS-based mapping, we are requested to obtain the correct
order of probes in a DNA sequence from a given set of fragments
or equivalently a hybridization matrix $A$. It is well-known that
the problem is formulated as the combinatorial problem of obtaining
a permutation of $A$'s columns so that the resulting matrix has the
consecutive-one property. If the data (the hybridization matrix)
is error free and includes enough information, then the above column
order determines the correct order of the probes uniquely.
Unfortunately this is no longer true if the data include errors,
which has been one of the popular research targets in computational
biology. Even if there is no error, ambiguities in the probe order
may still remain. This in fact happens by the lack of some information
of the data, but almost no further investigation was made previously.
In this paper, we define a measure of such imperfectness of the data
as a minimum amount of additional fragments which are needed to fix
the probe order uniquely. Several polynomial-time algorithms to compute
such additional fragments of minimum cost are presented.
-
id=2004-17
- The next bit test was introduced by Blum and Micali
and proved by Yao to be a universal test
for cryptographic pseudorandom generators. On the other hand,
no universal test for the cryptographic one-wayness of
functions (or permutations) is
known, though the existence of cryptographic pseudorandom generators
is equivalent to that of cryptographic one-way functions.
In the quantum computation model, Kashefi, Nishimura and Vedral
gave a sufficient condition of (cryptographic)
quantum one-way permutations and conjectured that the condition
would be necessary. In this paper, we relax their sufficient condition
and give a new condition that is necessary and sufficient for
quantum one-way permutations. Our condition can be regarded
as a universal test for quantum one-way permutations, since our
condition is described as a collection of stepwise tests similar to
the next bit test for pseudorandom generators.
-
id=2004-19
- While the original stable marriage problem requires all
participants to rank all members of the opposite sex in a
strict order, two natural variations are to allow for
incomplete preference lists and ties in the preferences.
Either variation is polynomially solvable, but it has
recently been shown to be NP-hard to find a maximum
cardinality stable matching when both of the variations are
allowed. It is easy to see that the size of any two stable
matchings differ by at most a factor of two, and so, an
approximation algorithm with a factor two is trivial. In
this paper, we give a randomized approximation algorithm
RandBrk and show that its expected approximation ratio is
at most $10/7 (< 1.4286)$ for a restricted but still NP-hard
case, where ties occur in only men's lists, each man writes
at most one tie, and the length of ties is two. We also show
that our analysis is nearly tight by giving a lower bound
$32/23 (> 1.3913)$ for RandBrk. Furthermore, we show that
these restrictions except for the last one can be removed
without increasing the approximation ratio too much.
-
id=2004-20
- Three partial orders, cut-size order, length order, and
operation order, defined between labeled multigraphs with
the same order are known to be equivalent. This paper extends
the result on edge-capacitated graphs, where the capacities
are real numbers, and it presents a proof of the equivalence
of the three relations. From this proof, it is also shown that
we can determine whether or not a given graph precedes another
given graph in polynomial time.
-
id=2004-22
- This paper studies the maximum load in the {\it approximated}
$d$-choice balls-and-bins game where the current load of each bin is
available only approximately. In the model of this game, we have $r$
thresholds $T_1,...,T_r$ $(0 < T_1 < \cdots < T_r)$
for an integer $r$
$(\geq 1)$. For each ball, we select $d$ bins and put the ball into
the bin of the lowest range, i.e., the bin of load $i$ such that
$T_k \leq i \leq T_{k+1}-1$ and no other selected bin has height less
than $T_k$. If there are two or more bins in the lowest range (i.e.,
their height is between $T_k$ and $T_{k+1}-1$), then we assume that
those bins cannot be distinguished and so one of them is selected
uniformly at random. We then estimate the maximum load for $n$ balls
and $n$ bins in this game. In particular, when we put the $r$ thresholds
at a regular interval of an appropriate $\Delta$, i.e.,
$T_r-T_{r-1} = \cdots = T_2 - T_1 = T_1 = \Delta$, the maximum load
$L(r)$ is given as $(r + O(1)) \sqrt[r+1]{\frac{r+1}{(d-1)^r} \ln n
/ \ln\left( \frac{r+1}{(d-1)^r} \ln n \right) }.$
The bound is also described as
$L(\Delta) \leq \{(1+o(1))\ln\ln n+O(1)\}\Delta/\ln((d-1)\Delta)$
using parameter $\Delta$. Thus, if $\Delta$ is a constant, this bound
matches the (tight) bound in the original $d$-choice model given
by Azar et al., within a constant factor. The bound is also tight
within a constant factor when $r=1$.
-
id=2004-23
- In a recent communication network, some mirror servers that
provide the same service as an original server are often
used. From the view of the network reliability, it is
important that a client can access to at least one of the
original or its mirror servers, even if some links or nodes
fail. Therefore, it is necessary to design a network so that
it ensures some independent routes between a client and a set
of servers that provide the same service. When a
communication network is modeled by a graph, the connectivity
between a client and some mirror servers can be measured by
NA(Node-to-Area)-edge(resp. vertex)-connectivity between a
vertex and a vertex subset (an area), which is equal to the
number of edge(resp. vertex)-independent paths between a
vertex and an area. In this paper, we focus on the network
design problem to increase the reliability of a current
network by adding the smallest number of links. This problem
can be formulated as the problem of augmenting a graph by
adding the smallest number of new edges to meet
NA-edge(vertex)-connectivity requirement. First, we prove
the NP-completeness of the problem to determine whether a
graph can be 1-NA-edge-connected by adding the given number
or less of edges. Next, we show that the problem of
augmenting a graph to be 2-NA-edge-connected by adding the
smallest edges can be solved in polynomial time.
-
id=2004-24
- It is known that the original Grover Search (GS) can be modified
to use a general value for the phase $\theta$ of the diffusion transform.
Then, if the number of answers is relatively large, this modified GS can
find one of the answers with probability one in a single iteration.
However, such a quick and error-free GS can only be possible if we can
initially adjust the value of $\theta$ correctly against the number of
answers, and this seems very hard in usual occasions. A natural question
now arises: Can we enjoy a merit even if GS is used without
such an adjustment? In this paper, we give a positive answer using
the balls-and-bins game in which the random sampling of bins is
replaced by the quantum sampling, i.e., a single round of modified GS.
It is shown that by using the quantum sampling:
(i) The maximum load can be improved quadratically for the static model
of the game and this improvement is optimal.
(ii) That is also improved to $O(1)$ for the continuous model
if we have a certain knowledge about the total number of balls
in the bins after the system becomes stable.
-
id=2004-25
- Cowen gave a universal compact routing algorithm with
a stretch factor of three and table-size of $O(n^{2/3}\log^{4/3}n)$
based on a simple and practical model.
(The table-size is later improved to $O(n^{1/2}\log^{3/2} n)$.)
This paper considers, using the same model, how the necessary table-size
differs if the stretch factor must be {\it less than} three.
It is shown that: (i)~There is a routing algorithm with a stretch factor
of two whose table-size is $(n-\sqrt{n}+2)\log n$.
(ii)~There is a network for which any routing algorithm that follows
the model and with a stretch factor of less than three needs
a table-size of $(n-2\sqrt{n})\log n$ in at least one node.
Thus, we can only reduce roughly an {\it additive} $\sqrt{n}\log n$
(i.e., $\sqrt{n}$ table-entries) from the trivial table-size of $n\log n$
which obviously enables shortest-path routing. Furthermore it turns out
that we can reduce only an additive $\log n$ (i.e., only one table-entry)
from the trivial $n\log n$ if we have to achieve a stretch factor of
less than {\it two}. Thus the algorithm (i) is (roughly) tight both
in its stretch factor and in its table-size.
-
id=2004-26
- Although many problems in MAX-SNP admit a PTAS for dense
graphs, that is not the case for Vertex Cover, which is
MAX-SNP hard even for dense graphs. This paper presents a
randomized approximation algorithm for Vertex Cover on dense
graphs, i.e., graphs whose average degree d is $\Omega(n)$. (i)
Our algorithm improves the best-known bound for the
approximation factor by Karpinski and Zelikovsky. For
example, our bound is $\frac{2}{1+ \frac{d}{2\Delta}}$ for
dense graphs such that $|E| \le \Delta(n - \Delta)$ where
$\Delta$ is the maximum degree. The improvement is especially
large when $d \approx \Delta$; if $d \ge \frac{2}{3}\Delta$ for
instance, our bound is at most 1.5 while the previous bound
approaches to 2.0 as $\frac{n}{\Delta}$ increases. (ii) It
achieves the same factor for a wider range of graphs, i.e.,
for the graphs whose $\Delta$ is $\Omega(n\frac{log log n}{log
n} )$. (iii) It is probably optimal in the sense that if we
can achieve a better approximation factor by $\delta > 0$ for
the above range of graphs, then we can achieve a factor of $2 -
\delta$ for general graphs.
-
id=2004-27
- 進化系統樹とは地球上の生物が、共通の祖先から進化したと考えた
時の、種間の進化的な関係を表現した木構造である。遺伝的な情報
から進化系統樹を推定する方法に対する研究はさかんに行われてき
た。また系統樹の一部に修正を加えたデータ構造を推定する研究も
近年行われきている。
これに対し、家系図は進化系統樹をさらに詳しくしたものと考える
ことができる。進化系統樹をグラフで表現すれば有向木になるのに
対し、家系図は入次数が2以下の非閉路的有向グラフとなる。本稿
では、与えられた2節点間の遺伝的距離を満足する家系図を全て列
挙する問題を考え、所望の家系図の全てが、節点数を増やすことな
く一つの有向グラフで表現できることを示し、それを得る$O(n^3)$
時間アルゴリズムを与える。
-
id=2004-28
- Let $s$ be the ratio of the cost for purchasing skis over the cost
for renting them. Then the famous result for the ski-rental problem
shows that skiers should buy their skis after renting them $(s-1)$
times, which gives us an optimal competitive ratio of $2-\frac{1}{s}$.
In practice, however, it appears that many skiers buy their skis
before this optimal point of time and also many skiers keep renting
them forever. In this paper we show that these behaviors of skiers are
quite reasonable by using an {\em average-case competitive ratio}. For
an exponential input distribution $f(t) = \lambda e^{-\lambda t}$,
optimal strategies are (i) if $\frac{1}{\lambda} \leq s$, then skiers
should rent their skis forever and (ii) otherwise should purchase them
after renting approximately $s^2\lambda \;\;(< s)$ times. Thus
average-case competitive analyses give us the result which differs
from the worst-case competitive analysis and also differs from the
traditional average cost analysis. Other distributions and related
problems are also discussed.
-
id=2004-29
- The oracle identification problem (OIP) was introduced by
Ambainis et. al., which is given as a set $S$ of $M$ oracles
and a hidden oracle $f$. Our task is to figure out which
oracle in $S$ is equal to the hidden $f$ by doing queries to
$f$. OIP includes several problems such as Grover Search as
special cases. In this paper, we design {\it robust}
algorithms, i.e., those which are tolerant against noisy
oracles, for OIP. Our results include: ($i$) For any oracle
set $S$ such that $|S|$ is polynomial in $N$, $O(\sqrt{N})$
queries are enough to identify the hidden oracle, which is
obviously optimal since this OIP includes Grover Search as a
special case. ($ii$) For the case that $|S| \le 2^{N^d} (d <
1)$, we design an algorithm whose query complexity is
$O(\sqrt{N \log M/ \log N})$ and matches the lower bound
proved before. ($iii$) We can furthermore design a robust
algorithm whose complexity changes smoothly between the
complexity of ($ii$) and the complexity of recovering all
information about the hidden oracle whose complexity is O(N)
as showed by Buhrman et. al. Thus our new algorithms are not
only robust but also their query complexities are even better
than the previous noiseless case.
-
id=2004-30
- The Haj\'os calculus is a nondeterministic procedure
which generates the class of non-3-colorable graphs.
Unless NP~$\neq$~co-NP, there must exist graphs which need exponential
steps to be constructed in the Haj\'os calculus, however it is not known.
In this paper, we propose new systems of graph calculus which generate
the class of non-3-colorable planar graphs and show its upper bound.
-
id=2004-31
- Let $s$ be the ratio of the cost for purchasing skis over the cost
for renting them. Then the famous result for the ski-rental problem
shows that skiers should buy their skis after renting them $(s-1)$
times, which gives us an optimal competitive ratio of $2-\frac{1}{s}$.
In practice, however, it appears that many skiers buy their skis
before this optimal point of time and also many skiers keep renting
them forever. In this paper we show that these behaviors of skiers are
quite reasonable by using an {\em average-case competitive ratio}. For
an exponential input distribution $f(t) = \lambda e^{-\lambda t}$,
optimal strategies are (i) if $\frac{1}{\lambda} \leq s$, then skiers
should rent their skis forever and (ii) otherwise should purchase them
after renting approximately $s^2\lambda \;\;(< s)$ times. Thus
average-case competitive analyses give us the result which differs
from the worst-case competitive analysis and also differs from the
traditional average cost analysis. Other distributions and related
problems are also discussed.
-
id=2004-32
- 安定結婚問題は二部グラフにおけるマッチング問題の一種である.
複数の男女がおり,各人は異性を自分の好みで順序づけした希望リ
ストを持っている.その希望リストに基づいて「安定性」を満たす
マッチング(結婚)を求めるのが,安定結婚問題である.この問題は,
アメリカの研修医配属への応用が有名であるが,近年日本の研修医
配属でも利用し始められた.本稿では,安定結婚問題の基本的性質
や応用例を紹介する.
-
id=2004-34
- For networks employing shortest-path routing, we introduce a
new recovery scheme that needs only one extra backup routing
table. By precomputing this backup table, the network recovers
from any single link-failure immediately after the failure
occurs. To compute the backup routing table for this scheme,
we use the almost-linear-time algorithm to solve {r, v}-problem,
which is a variation of the best swap problem,
presented by Nardelli, et al. We further show that the same
solution can be computed in exactly linear time if the
underlying graph is unweighted.