arXiv subjects

Hironori Kiya

Publications and source records attributed to Hironori Kiya.

7 recordsLinked to original sources

arXiv2026

A Moderatorless Protocol for WEREWOLF

Social deduction games, or hidden-role games, are multiplayer games in which players are assigned private roles and act under asymmetric information about other players' roles and actions. In the canonical example Werewolf, werewolves conceal their roles and mislead the other players, while the seer can obtain role information about a chosen player. Thus, a central functionality of such games is controlling which players can access which information. In typical play, this control is implemented by a trusted human moderator, who assigns roles, mediates secret actions, and reveals outcomes. This reliance raises the barrier to participation and introduces a trusted third party as a single point of failure. In this work, we show that Werewolf can be played without a moderator or any digital device, using only ordinary playing cards. Our construction maintains a shared pool of cards that is observable to all players and manipulated according to a common public procedure, while its interpretation depends on each player's private role. This induces role-dependent views from a single public sequence of card operations. Consequently, even without private messages, werewolves can identify one another and coordinate, and the seer can test whether a chosen player is a werewolf in each round. The proposed implementation is built from card-based physical cryptographic primitives, such as face-down commitments and verifiable shuffles, and higher-level subprotocols for intra-role information sharing, secret action designation, and attribute testing. These subprotocols implement the moderator's core functions while keeping all card operations public and auditable under standard assumptions on physical card operations. We show that the resulting complete moderatorless implementation of Werewolf scales to an arbitrary number n of players using O(n^3) cards.

cs.CR↗

arXiv2025

Finding a HIST: Chordality, Structural Parameters, and Diameter

A homeomorphically irreducible spanning tree (HIST) is a spanning tree with no degree-2 vertices, serving as a structurally minimal backbone of a graph. While the existence of HISTs has been widely studied from a structural perspective, the algorithmic complexity of finding them remains less understood. In this paper, we provide a comprehensive investigation of the HIST problem from both structural and algorithmic viewpoints. We present a simple characterization that precisely describes which chordal graphs of diameter at most~3 admit a HIST, leading to a polynomial-time decision procedure for this class. In contrast, we show that the problem is NP-complete for strongly chordal graphs of diameter~4. From the perspective of parameterized complexity, we establish that the HIST problem is W[1]-hard when parameterized by clique-width, indicating that the problem is unlikely to be efficiently solvable in general dense graphs. On the other hand, we present fixed-parameter tractable (FPT) algorithms when parameterized by treewidth, modular-width, or cluster vertex deletion number. Specifically, we develop an $O^*(4^{k})$-time algorithm parameterized by modular-width~$k$, and an FPT algorithm parameterized by the cluster vertex deletion number based on kernelization techniques that bound clique sizes while preserving the existence of a HIST. These results together provide a clearer understanding of the structural and computational boundaries of the HIST problem.

cs.CC↗

arXiv2024

Enforce and selective operators of combinatorial games

We consider an {\em enforce operator} on impartial rulesets similar to the Muller Twist and the comply/constrain operator of Smith and St\u anic\u a, 2002. Applied to the rulesets A and B, on each turn the opponent enforces one of the rulesets and the current player complies, by playing a move in that ruleset. If the outcome table of the enforce variation of A and B is the same as the outcome table of A, then we say that A dominates B. We find necessary and sufficient conditions for this relation. Additionally, we define a {\em selective operator} and explore a distributive-lattice-like structure within applicable rulesets. Lastly, we define nim-values under enforce-rulesets, and establish that the Sprague-Grundy theory continues to hold, along with illustrative examples.

math.CO↗

arXiv2023

Turning Tiles is PSPACE-complete

In combinatorial game theory, the winning player for a position in normal play is analyzed and characterized via algebraic operations. Such analyses define a value for each position, called a game value. A game (ruleset) is called universal if any game value is achievable in some position in a play of the game. Although the universality of a game implies that the ruleset is rich enough (i.e., sufficiently complex), it does not immediately imply that the game is intractable in the sense of computational complexity. This paper proves that the universal game Turning Tiles is PSPACE-complete.

cs.DM↗

arXiv2023

Sequentially Swapping Tokens: Further on Graph Classes

We study the following variant of the 15 puzzle. Given a graph and two token placements on the vertices, we want to find a walk of the minimum length (if any exists) such that the sequence of token swappings along the walk obtains one of the given token placements from the other one. This problem was introduced as Sequential Token Swapping by Yamanaka et al. [JGAA 2019], who showed that the problem is intractable in general but polynomial-time solvable for trees, complete graphs, and cycles. In this paper, we present a polynomial-time algorithm for block-cactus graphs, which include all previously known cases. We also present general tools for showing the hardness of the problem on restricted graph classes such as chordal graphs and chordal bipartite graphs. We also show that the problem is hard on grids and king's graphs, which are the graphs corresponding to the 15 puzzle and its variant with relaxed moves.

cs.DS↗

arXiv2022

Winner Determination Algorithms for Graph Games with Matching Structures

Cram, Domineering, and Arc Kayles are well-studied combinatorial games. They are interpreted as edge-selecting-type games on graphs, and the selected edges during a game form a matching. In this paper, we define a generalized game called Colored Arc Kayles, which includes these games. Colored Arc Kayles is played on a graph whose edges are colored in black, white, or gray, and black (resp., white) edges can be selected only by the black (resp., white) player, although gray edges can be selected by both black and white players. We first observe that the winner determination for Colored Arc Kayles can be done in $O^*(2^n)$ time by a simple algorithm, where $n$ is the order of a graph. We then focus on the vertex cover number, which is linearly related to the number of turns, and show that Colored Arc Kayles, BW-Arc Kayles, and Arc Kayles are solved in time $O^*(1.4143^{τ^2+3.17τ})$, $O^*(1.3161^{τ^2+4τ})$, and $O^*(1.1893^{τ^2+6.34τ})$, respectively, where $τ$ is the vertex cover number. Furthermore, we present an $O^*((n/ν+1)^ν)$-time algorithm for Arc Kayles, where $ν$ is neighborhood diversity. We finally show that Arc Kayles on trees can be solved in $O^* (2^{n/2})(=O(1.4143^n))$ time, which improves $O^*(3^{n/3})(=O(1.4423^n))$ by a direct adjustment of the analysis of Bodlaender et al.'s $O^*(3^{n/3})$-time algorithm for Node Kayles.

cs.DS↗

arXiv2019

Computational Complexity of Hedonic Games on Sparse Graphs

The additively separable hedonic game (ASHG) is a model of coalition formation games on graphs. In this paper, we intensively and extensively investigate the computational complexity of finding several desirable solutions, such as a Nash stable solution, a maximum utilitarian solution, and a maximum egalitarian solution in ASHGs on sparse graphs including bounded-degree graphs, bounded-treewidth graphs, and near-planar graphs. For example, we show that finding a maximum egalitarian solution is weakly NP-hard even on graphs of treewidth 2, whereas it can be solvable in polynomial time on trees. Moreover, we give a pseudo fixed parameter algorithm when parameterized by treewidth.

cs.CC↗