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## Publications

Publications (143)

The classic Tower of Hanoi puzzle involves moving a set of disks on three pegs. The number of moves required for a given number of disks is easy to determine, but when the number of pegs is increased to four or more, this becomes more challenging. After 75 years, the answer for four pegs was resolved only recently, and this time complexity question...

The problem called "String reconstruction from substrings" is a mathematical model of sequencing by hybridization that plays an important role in DNA sequencing. In this problem, we are given a blackbox oracle holding an unknown string ${\mathcal X}$ and are required to obtain (reconstruct) ${\mathcal X}$ through "substring queries" $Q(S)$. $Q(S)$...

This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is \(n \lg n - 1.4427n + O(\log n)\). For many efficient algorithms, the first \(n\lg n\) term is easy to achieve and our focus is on the (negative) constant factor of the linear term. The current best value is \(-1.3...

This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is $n \lg n - 1.4427n + O(\log n)$. For many efficient algorithms, the first $n\lg n$ term is easy to achieve and our focus is on the (negative) constant factor of the linear term. The current best value is $-1.3999$...

This paper considers the quantum query complexity of almost all functions in the set \({\mathcal{F}}_{N,M}\) of \({N}\)-variable Boolean functions with on-set size \({M (1\le M \le 2^{N}/2)}\), where the on-set size is the number of inputs on which the function is true. The main result is that, for all functions in \({\mathcal{F}}_{N,M}\) except it...

In this paper we establish an algorithmic framework between bin packing and strip packing, with which strip packing can be very well approximated by applying some bin packing algorithms. More precisely we obtain the following results: (1) Any off-line bin packing algorithm can be applied to strip packing maintaining almost the same asymptotic worst...

We study a variant of online bin packing problem, in which there are two types of bins: \((1,1)\) and \((2,R)\) , i.e., unit size bin with cost 1 and size 2 bin with cost \(R > 1\) , the objective is to minimize the total cost occurred when all the items are packed into the two types of bins. When \(R > 3\) , the offline version of this problem is...

In this paper, we study the train delivery problem which is a generalization of the bin packing problem, and is also equivalent to a one dimensional version of the vehicle routing problem with unsplittable demands. We give an APTAS for the general problem with time complexity O(n O(ε -4 ) ), which is better than the previous one O(n (1 ε) O(1 ε) ),...

In the three-dimensional (3D) strip packing problem, we are given a set of 3D rectangular items and a 3D box B. The goal is to pack all the items in B such that the height of the packing is minimized. We consider the most basic version of the problem, where the items must be packed with their edges parallel to the edges of B and cannot be rotated....

We study a variant of online bin packing problem, in which there are two types of bins: (1,1) and (2,R), i.e., unit size bin with cost 1 and size 2 bin with cost R > 1, the objective is to minimize the total cost occurred when all the items are packed into the two types of bins. It is not difficult to see that the offline version of the problem is...

The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only “balanced” or “tilted” information and that we know the number k of false coins in advance. The balance scale can be modeled by a certain type of oracle and its query complexity is a meas...

This paper investigates the number of quantum queries made to solve the problem of reconstructing an unknown string from its substrings in a certain query model. More concretely, the goal of the problem is to identify an unknown string S by making queries of the following form: “Is s a substring of S?”, where s is a query string over the given alph...

The Hospitals/Residents problem is a many-to-one extension of the stable marriage problem. In its instance, each hospital specifies a quota, i.e., an upper bound on the number of positions it provides. It is well-known that in any instance, there exists at least one stable matching, and finding one can be done in polynomial time. In this paper, we...

Manlove and O’Malley [9] proposed the Student-Project Allocation Problem with Preferences over Projects (SPA-P). They proved
that the problem of finding a maximum stable matching in SPA-P is APX-hard and gave a polynomial-time 2-approximation algorithm.
In this paper, we give an improved upper bound of 1.5 and a lower bound of $21/19 \ (>1.1052)$21...

The stable marriage problem is a classical matching problem introduced by Gale and Shapley. It is known that for any instance, there exists a solution, and there is a polynomial time algorithm to find one. However, the matching obtained by this algorithm is man-optimal, that is, the matching is favorable for men but unfavorable for women, (or, if w...

It is known that online knapsack is not competitive. This negative result remains true even if items are removable. In this paper we consider online removable knapsack with resource augmentation, in which we hold a knapsack of capacity R⩾1 and aim at maintaining a feasible packing to maximize the total profit of items packed into the knapsack. Both...

The problem of finding a largest stable matching where preference lists may include ties and unacceptable partners (MAX SMTI) is known to be NP-hard. It cannot be approximated within 33=29 (> 1:1379) unless P=NP, and the current best approximation algorithm achieves the ratio of 1:5. MAX SMTI remains NP-hard even when preference lists of one side d...

The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only “balanced” or “tilted” information and that we know the number k of false coins in advance. The balance scale can be modeled by a certain type of oracle and its query complexity is a meas...

In this article, we consider isolated cliques and isolated dense subgraphs. For a given graph G , a vertex subset S of size k (and also its induced subgraph G ( S )) is said to be c -isolated if G ( S ) is connected to its outside via less than ck edges. The number c is sometimes called the isolation factor . The subgraph appears more isolated if t...

This paper considers the query complexity of the functions in the family F_{N,M} of N-variable Boolean functions with onset size M, i.e., the number of inputs for which the function value is 1, where 1<= M <= 2^{N}/2 is assumed without loss of generality because of the symmetry of function values, 0 and 1. Our main results are as follows: (1) There...

In the stable marriage problem that allows incomplete preference lists, all stable matchings for a given instance have the same size. However, if we ignore the stability, there can be larger matchings. Biró et al. defined the problem of finding a maximum cardinality matching that contains minimum number of blocking pairs. They proved that this prob...

The main objective of this paper is to show that the quantum query complexity Q(f) of an N-bit Boolean function f is bounded by a function of a simple and natural parameter, i.e., M = |{x|f(x) = 1}| or the size of f’s on-set. We prove that: (i) For \(poly(N)\le M\le 2^{N^d}\) for some constant 0 < d < 1, the upper bound of Q(f) is \(O(\sqrt{N\log M...

In this Chapter, our focus is the efficiency of computation with quantum oracles whose answers are correct only with probability
1/2 + ε. In real-world applications, quantum oracles might be realized from quantumization of probabilistic algorithms which
are object to error in the success probability. Thus, designing efficient quantum algorithms for...

We introduce the Oracle Identification Problem (OIP), which includes many problems in oracle computation such as those of
Grover search and Bernstein-Vazirani as its special cases. We give general upper and lower bounds on the number of oracle
queries of OIP. Thus, our results provide general frameworks for analyzing the quantum query complexity of...

Constructing k independent sessions between k source-sink pairs with the help of a linear operation at each vertex is one of the most standard problems in network coding. For an unbounded k, this is known to be NP-hard. Very recently, a polynomial-time algorithm was given for k = 2 (Wang and Shroff, ISIT 2007), but was open for a general (constant)...

The online removable square packing problem is a two-dimen-sional version of the online removable Knapsack problem. For a
sequence of squares with side length at most 1, we are requested to pack a subset of them into a unit square bin in an online
fashion where the online player can decide whether to take the current square or not and which squares...

In this paper, we study the following knapsack problem: Given a list of squares with profits, we are requested to pack a sublist of them into a rectangular bin (not a unit square bin) to make profits in the bin as large as possible. We first observe there is a Polynomial Time Approximation Scheme (PTAS) for the problem of packing weighted squares i...

Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86}, the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently, \cite[ICALP'07]{INRY07} found that the unbounded-error {\em quantum} communication complexity in the {\em one-way commu...

This paper studies the gap between quantum one-way communication complexity Q(f) and its classical counterpart C(f), under the unbounded-error setting, i.e., it is enough that the success probability is strictly greater than 1/2. It is proved that for any (total or partial) Boolean function f, Q(f) = ⌈C(f)/2 ⌉, i.e., the former is always exactly on...

The stable marriage problem is a classical matching problem introduced by Gale and Shapley. It is known that for any instance, there exists a solution, and there is a polynomial time algorithm to find one. However, the matching obtained by this algorithm is man-optimal, that is, the matching is preferable for men but unpreferable for women, (or, if...

The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed. It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially we can obtain a 2-approximation algorithm.
In this article, we give the first nontrivial result fo...

A spreadsheet, especially MS Excel, is probably one of the most popular software applications for personal-computer users
and gives us convenient and user-friendly tools for drawing tables. Using spreadsheets, we often wish to draw several vertical
and horizontal black lines on selective gridlines to enhance the readability of our spreadsheet. Such...

A box graph is the intersection graph of a finite set of orthogonal rectangles in the plane. The problem of whether or not
the maximum independent set problem (MIS for short) for box graphs can be approximated within a substantially sub-logarithmic
factor in polynomial time has been open for several years. We show that for box graphs on n vertices...

The oracle identification problem (OIP) was introduced by Ambainis et al. [A. Ambainis, K. Iwama, A. Kawachi, H. Masuda, R.H. Putra, S. Yamashita, Quantum identification of boolean oracles, in: Proc. of STACS’04, in: LNCS, vol. 2996, 2004, pp. 105–116]. It is given as a set S of M oracles and a blackbox oracle f. Our task is to figure out which ora...

A spreadsheet, especially MS Excel, is probably one of the most popular software applications for personal-computer users and gives us convenient and user-friendly tools for drawing tables. Using spreadsheets, we often wish to draw several vertical and horizontal black lines on selective gridlines to enhance the readability of our spreadsheet. Such...

Since quantum information is continuous, its handling is sometimes surprisingly harder than the classical counterpart. A typical example is cloning; making a copy of digital information is straightforward but it is not possible exactly for quantum information. The question in this paper is whether or not quantum network coding is possible. Its clas...

Abstract We consider the problem of finding a stable matching,of maximum,size when,both ties and unacceptable partners are allowed in preference lists. This problem is known,to be APX-hard, and the current best known approximation algorithm achieves the approximation ratio 2 � c , √N ,w here c is some positive constant. In this paper, we give a 1.8...

In the three dimensional strip packing problem, we are given a set of three-dimensional rectangular items I = {(xi, yi, zi) : i = 1, ..., n} and a three dimensional box B. The goal is to pack all the items in the box B without any overlap, such that the height of the packing is minimized. We consider the most basic version of the problem, where the...

Abstract It is known that online knapsack is not competitive. This negative result remains true even if the items are removable. In this paper we consider online removable knapsack with resource augmentation, in which we hold a knapsack of capacity R � 1.0 and aim at main- taining a feasible packing to maximize the total weight of the items packed....

In the stable roommates problem, we are given 2N men and each person's pref-erence list. We are asked to find a stable matching, namely, a set of N pairs satisfying the stability condition. This problem is known to be solved in polynomial time; more precisely, there is a polynomial-time algorithm to find a stable matching for a given instance, or t...

Network coding is often explained by using a small network model called Butterfly. In this network, there are two flow paths, s_1 to t_1 and s_2 to t_2, which share a single bottleneck channel of capacity one. So, if we consider conventional flow (of liquid, for instance), then the total amount of flow must be at most one in total, say 1/2 for each...

In this paper, we study the 3D strip packing problem in which we are given a list of 3-dimensional boxes and required to pack all of them into a 3-dimensional strip with length 1 and width 1 and unlimited height to minimize the height used. Our results are below: i) we give an approximation algorithm with asymptotic worst-case ratio 1.69103, which...

In this paper we establish a general algorithmic framework between bin packing and strip packing, with which we achieve the same asymptotic bounds by applying bin packing algorithms to strip packing. More precisely we obtain the following results: (1) Any offline bin packing algorithm can be applied to strip packing maintaining the same asymptotic...

An (n,1,p)-quantum random access (QRA) coding, introduced by Ambainis et al (1999 ACM Symp. Theory of Computing p 376), is the following communication system: the sender which has n-bit information encodes his/her information into one qubit, which is sent to the receiver. The receiver can recover any one bit of the original n bits correctly with pr...

An instance of the classical stable marriage problem requires all participants to submit a strictly ordered preference list containing all members of the opposite sex. However, considering applications in real-world, we can think of two natural relaxations, namely, incomplete preference lists and ties in the lists. Either variation leaves the probl...

An (n,1,p)-quantum random access (QRA) coding, introduced by Ambainis, Nayak, Ta-shma and Vazirani in ACM Symp. on Theory of Computing 1999, is the following communication system: The sender which has n-bit information encodes his/her information into one qubit, which is sent to the receiver. The receiver can recover any one bit of the original n b...

In STS-based mapping, it is necessary to obtain the correct order of probes in a DNA sequence from a given set of fragments or an 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 a consecutive-one property....

It is said that a set L
1 in a class C
1
approximates a set L
2 in a class C
2 if L
1 is a subset of L
2. Approximation L
1 is said to be optimal if there is no approximation L1 such that L1 L
1 and L1 - L
1 is infinite. When C
1=P and C
2=NP, it is known that there is no optimal approximation under a quite general condition unless P=NP. In this pa...

At the heart of the Goldreich-Levin theorem is the problem of determining an n-bit string a by making queries to two oracles, referred to as IP (inner product) and EQ (equivalence). The IP oracle, on input x, returns a bit that is biased towards a•x (the modulo two inner product of a with x) in the following sense. For a random x, the probability t...

The online removable square packing problem is a two dimensional version of the online removable Knapsack problem. For a sequence
of squares with side length at most 1, we are requested to pack a subset of them into a unit square in an online fashion where
the online player can decide whether to take the current square or not and which squares curr...

Since quantum information is continuous, its handling is sometimes surprisingly harder than the classical counterpart. A typical example is cloning; making a copy of digital information is straightforward but it is not possible exactly for quantum information. The question in this paper is whether or not quantum network coding is possible. Its clas...

We consider the problem of finding a stable matching of maximum size when both ties and unacceptable partners are allowed
in preference lists. This problem is NP-hard and the current best known approximation algorithm achieves the approximation
ratio 2 - c[(log N)/(N)]2 - c{{\rm log N} \over {N}}, where c is an arbitrary positive constant and N is...

This paper reviews researches on quantum oracle computations when oracles are not perfect, i.e., they may return wrong answers. We call such oracles biased oracles, and discuss the formal model of them. Then we provide an intuitive explanation how quantum search with biased oracles by Høyer, et al.(2003) works. We also review the method, by Buhrman...

For a given graph G of n vertices and m edges, a clique S of size k is said to be c-isolated if there are at most ck outgoing edges from S. It is shown that this parameter c is an interesting measure which governs the complexity of finding cliques. In particular, if c is a constant, then we can enumerate all c-isolated maximal cliques in linear tim...

We introduce a new recovery scheme that needs only one extra backup routing table for networks employing shortest-path routing. 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 an almost linear time algorithm to solv...

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 [1]. (The table-size is later improved to O(n(1/2) log(3/2) n) [11].) This paper considers, using the same model, how the necessary table-size differs if the stretch factor must be less than th...

An oracle with bias e is an oracle that answers queries correctly with a probability of at least 1/2+e. In this paper, we study the upper and lower bounds of quantum query complexity of oracles with bias e. For general upper bounds, we show that for any quantum algorithm solving some problem with high probability using T queries of perfect quantum...

We consider the problem of finding a stable matching of maximum size when both ties and unacceptable partners are allowed in preference lists. This problem is NP-hard and the current best known approximation algorithm achieves the approximation ratio 2−c(log N)/N, where c is an arbitrary positive constant and N is the number of men in an input. In...

The oracle identification problem (OIP) was introduced by Ambainis et al. \cite{AIKMRY04}. It is given as a set $S$ of $M$ oracles and a blackbox oracle $f$. Our task is to figure out which oracle in $S$ is equal to the blackbox $f$ by making queries to $f$. OIP includes several problems such as the Grover Search as special cases. In this paper, we...

This paper studies the maximum load in the 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 < ... < T
r
) for an integer r (≥ 1). For each ball, we select d bins and put the ball into the bin of the lowest range, i.e., t...

SUMMARY An instance of the classical stable marriage problem re- quires all participants to submit a strictly ordered preference list contain- ing all members of the opposite sex. However, considering applications in real-world, we can think of two natural relaxations, namely, incomplete preference lists and ties in the lists. Either variation leav...

The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2N
ones, to determine which oracle in S is the current black-box oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the original Grover search and the Bernstein-Vazira...

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...

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 propert...

Suppose that some particular link in the Internet is currently
congested.
A natural solution is to try to make packets bypass that link.
This can be done by increasing the cost of that link intentionally,
say from a
1 to a
2, since the Internet uses shortest-path
routing. Unfortunately, however, this often causes temporary loops
for packet travelin...

This paper introduces a simple but nontrivial set of local transformation rules for designingControl-NOT(CNOT)-based combinatorial circuits. We also provide a proof that the rule set iscomplete, namely, for any two equivalent circuits,S
1 andS
2, there is a sequence of transformations, each of them in the rule set, which changesS
1 toS
2. Two appli...

Fork functionsf
1, ...f
k, ak-tuple (x
1, ...x
k) such thatf
1(x
1)=...=f
k(x
k) is called a claw off
1, ...,f
k. In this paper, we construct a new quantum claw-finding algorithm for three functions that is efficient when the numberM of intermediate solutions is small. The known quantum claw-finding algorithm for three functions requiresO(N
7/8 log...

The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed.
It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially
a factor two approximation.
In this paper, we give the first nontrivial result for approximation...

We consider instances of the classical stable marriage problem in which persons may include ties in their preference lists. We show that, in such a setting, strong lower bounds hold for the approximability of each of the problems of finding an egalitarian, minimum regret and sex-equal stable matching. We also consider stable marriage instances in w...

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...

It is known that the original Grover Search (GS) can be modified to use a general value for the phase θ 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 initia...

Our problem is to evaluate a multi-valued Boolean function $F$ through oracle calls. If $F$ is one-to-one and the size of its domain and range is the same, then our problem can be formulated as follows: Given an oracle $f(a,x): \{0,1\}^n\times\{0,1\}^n \to \{0,1\}$ and a fixed (but hidden) value $a_0$, we wish to obtain the value of $a_0$ by queryi...

For networks employing shortest-path routing, we introduce a new re-covery scheme which needs only one backup routing table. By precomputing this backup table, the network recovers from any single link-failure imme-diately after the failure occurs. It is shown that this scheme always works if the network is given as a two-edge-connected symmetric d...

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...

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 in...

This paper gives a simple but nontrivial set of local transformation rules for Control-NOT(CNOT)-based combinatorial circuits. It is shown that this rule set is complete, namely, for any two equivalent circuits, S 1 and S 2 , there is a sequence of transformations, each of them in the rule set, which changes S 1 to S 2 . Our motivation is to use th...

The main purpose of this paper is to show that we can ex- ploit the difference in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficien- cies. It is shown that, for each n, there is a finite language L which contains sentences of length up to O(n
c+1) such that: (i) There is a one...

The stable marriage problem has received considerable attention both due to its practical applications as well as its mathematical structure. While the original problem has all participants rank all members of the opposite sex in a strict order of preference, two natural variations are to allow for incomplete preference lists and ties in the prefer...

The Stable Marriage Problem and its many variants have been widely studied in the literature (Gusfield and Irving, The Stable Marriage Problem: Structure and Algorithms, MIT Press, Cambridge, MA, 1989; Roth and Sotomayor, Two-sided matching: a study in game-theoretic modeling and analysis, Econometric Society Monographs, vol. 18, Cambridge Universi...

This paper gives a simple but nontrivial set of local transformation rules for CNOT-based quantum circuits. It is shown that this rule set is complete, namely for any two equivalent circuits, S1andS2 , there is a sequence of transformations, each of them in the rule set, which changesS1 to S2. This rule set can be used for incremental circuit optim...

At each step of the online independent set problem, we axe given a vertex v and its edges to the previously given vertices. We are to decide whether or not to select v as a member of an independent set. Our goal is to maximize the size of the independent set. It is not difficult to see that no online algorithm can attain a performance ratio better...

The main purpose of this paper is to show that we can exploit the difference (l1-norm and l2-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It is shown that there is a finite language L which contains sentences of length up to O(nc-1} such that: (i) There is a...

This paper gives a simple but nontrivial set of local transformation rules for control-NOT (CNOT)-based combinatorial circuits. It is shown that this rule set is complete, namely, for any two equivalent circuits, S<sub>1</sub> and S<sub>2</sub>, there is a sequence of transformations, each of them in the rule set, which changes S<sub>1</sub> to S<s...

We propose a new framework for stateless auto-configuration of IPv6 site-local addresses with “zero configuration.” When a router is connected to a link as the first router, it becomes the link leader and generates an address prefix with randomly generated 16-bit subnet ID for the segment. In order to assure the uniqueness of the prefix addresses,...