arXiv subjects

Kazuya Okamoto

Publications and source records attributed to Kazuya Okamoto.

3 recordsLinked to original sources

arXiv2026

Analytical derivation of a three-dimensional fundamental diagram for a real-valued max-plus particle system

We study a real-valued max-plus particle system on a finite periodic lattice. Its three-dimensional fundamental diagram relates the mean flow to two densities: the conserved particle density and a second density defined by a local state function. We prove that the deviation from the diagram tends to zero for arbitrary initial data with all state values in [0,1]. The proof uses two nonnegative local quantities and their evolution relations. For rational initial data with all state values in $[0,1]$, the orbit is eventually periodic, and the fundamental-diagram relation holds exactly on the periodic orbit.

nlin.CG↗

arXiv2026

Three-dimensional Fundamental Diagrams of Five-neighbor Particle Cellular Automata

We analyze five-neighbor particle cellular automata whose conventional two-dimensional fundamental diagrams are multivalued, but whose mean flow is uniquely determined by introducing a second density. We first consider binary rules for which the second density is conserved, and then examine rules for which the second density is not conserved but converges asymptotically. These examples give three-dimensional fundamental diagrams in which the mean flow is determined by the particle density and the second density. We then investigate whether this single-valued structure is preserved under real-valued max-plus extensions. There are some rules where two different max-plus extensions are introduced, and numerical simulations show that both extensions preserve the same single-valued three-dimensional fundamental diagram. These observations imply that, in constructing real-valued max-plus extensions, it is important to choose the flux function and the second density consistently.

physics.soc-ph↗

arXiv2020

Strongly Stable and Maximum Weakly Stable Noncrossing Matchings

In IWOCA 2019, Ruangwises and Itoh introduced stable noncrossing matchings, where participants of each side are aligned on each of two parallel lines, and no two matching edges are allowed to cross each other. They defined two stability notions, strongly stable noncrossing matching (SSNM) and weakly stable noncrossing matching (WSNM), depending on the strength of blocking pairs. They proved that a WSNM always exists and presented an $O(n^{2})$-time algorithm to find one for an instance with $n$ men and $n$ women. They also posed open questions of the complexities of determining existence of an SSNM and finding a largest WSNM. In this paper, we show that both problems are solvable in polynomial time. Our algorithms are applicable to extensions where preference lists may include ties, except for one case which we show to be NP-complete. This NP-completeness holds even if each person's preference list is of length at most two and ties appear in only men's preference lists. To complement this intractability, we show that the problem is solvable in polynomial time if the length of preference lists of one side is bounded by one (but that of the other side is unbounded).

cs.DS↗