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Yuta Nozaki

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4 papers

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TCS Journal 2025 Journal Article

Reconfiguration and enumeration of optimal cyclic ladder lotteries

Yuta Nozaki
Kunihiro Wasa
Katsuhisa Yamanaka

A ladder lottery, known as “Amidakuji” in Japan, is a common way to decide an assignment at random. In this paper, we investigate reconfiguration and enumeration problems of cyclic ladder lotteries. First, when a permutation π and an optimal displacement vector x are given, we investigate the reconfiguration and enumeration problems of the “optimal” cyclic ladder lotteries of π and x. Next, for a given permutation π we consider reconfiguration and enumeration problems of the optimal displacement vectors of π.

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TCS Journal 2023 Journal Article

On reachable assignments under dichotomous preferences

Takehiro Ito
Naonori Kakimura
Naoyuki Kamiyama
Yusuke Kobayashi
Yuta Nozaki
Yoshio Okamoto
Kenta Ozeki

We consider the problem of determining whether a target item assignment can be reached from an initial item assignment by a sequence of pairwise exchanges of items between agents. In particular, we consider the situation where each agent has a dichotomous preference over the items, that is, each agent evaluates each item as acceptable or unacceptable. Furthermore, we assume that communication between agents is limited, and the relationship is represented by an undirected graph. Then, a pair of agents can exchange their items only if they are connected by an edge and the involved items are acceptable. We prove that this problem is PSPACE -complete even when the communication graph is complete (that is, every pair of agents can exchange their items), and this problem can be solved in polynomial time if an input graph is a tree.

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SODA Conference 2022 Conference Paper

Monotone edge flips to an orientation of maximum edge-connectivity à la Nash-Williams

Takehiro Ito
Yuni Iwamasa
Naonori Kakimura
Naoyuki Kamiyama
Yusuke Kobayashi 0001
Shun-ichi Maezawa
Yuta Nozaki
Yoshio Okamoto

We initiate the study of k -edge-connected orientations of undirected graphs through edge flips for k ≥ 2. We prove that in every orientation of an undirected 2 k -edge-connected graph, there exists a sequence of edges such that flipping their directions one by one does not decrease the edge-connectivity, and the final orientation is k -edge-connected. This yields an “edge-flip based” new proof of Nash-Williams' theorem: an undirected graph G has a k -edge-connected orientation if and only if G is 2 k -edge-connected. As another consequence of the theorem, we prove that the edge-flip graph of k -edge-connected orientations of an undirected graph G is connected if G is (2 k + 2)-edge-connected. This has been known to be true only when k = 1.

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AAAI Conference 2022 Conference Paper

Reforming an Envy-Free Matching

Takehiro Ito
Yuni Iwamasa
Naonori Kakimura
Naoyuki Kamiyama
Yusuke Kobayashi
Yuta Nozaki
Yoshio Okamoto
Kenta Ozeki

We consider the problem of reforming an envy-free matching when each agent is assigned a single item. Given an envy-free matching, we consider an operation to exchange the item of an agent with an unassigned item preferred by the agent that results in another envy-free matching. We repeat this operation as long as we can. We prove that the resulting envy-free matching is uniquely determined up to the choice of an initial envy-free matching, and can be found in polynomial time. We call the resulting matching a reformist envy-free matching, and then we study a shortest sequence to obtain the reformist envy-free matching from an initial envy-free matching. We prove that a shortest sequence is computationally hard to obtain even when each agent accepts at most four items and each item is accepted by at most three agents. On the other hand, we give polynomial-time algorithms when each agent accepts at most three items or each item is accepted by at most two agents. Inapproximability and fixed-parameter (in)tractability are also discussed.

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