arXiv subjects

Kritkorn Karntikoon

Publications and source records attributed to Kritkorn Karntikoon.

6 recordsLinked to original sources

arXiv2026

The $s$-Energy and Its Applications

Many multi-agent systems evolve by repeatedly updating each state to a weighted average of its neighbors, a process known as averaging dynamics, whose behavior becomes difficult to analyze when the interaction network varies over time. In recent years, the $s$-energy has emerged as a useful tool for bounding the convergence rates of such systems, complementing the classical techniques that rely on fixed graphs. We derive new bounds on the $s$-energy under minimal connectivity assumptions. As a consequence, we obtain convergence guarantees for several models of collective dynamics and resolve a number of open questions in the areas. Our results highlight the dependence of the $s$-energy on the connectivity of the underlying networks and use it to explain the exponential gap in the convergence rates of stationary and time-varying consensus systems.

math.OC↗

arXiv2025

First Passage Percolation with Queried Hints

Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is noisy, uncertain, and expensive to obtain. In this work, we study how much of that information needs to be queried in order to obtain an approximately optimal solution to the relevant problem. In particular, we focus on the shortest path problem in graphs with dynamic edge costs. We adopt the $\textit{first passage percolation}$ model from probability theory wherein a graph $G'$ is derived from a weighted base graph $G$ by multiplying each edge weight by an independently chosen random number in $[1, ρ]$. Mathematicians have studied this model extensively when $G$ is a $d$-dimensional grid graph, but the behavior of shortest paths in this model is still poorly understood in general graphs. We make progress in this direction for a class of graphs that resemble real-world road networks. Specifically, we prove that if $G$ has a constant continuous doubling dimension, then for a given $s-t$ pair, we only need to probe the weights on $((ρ\log n )/ ε)^{O(1)}$ edges in $G'$ in order to obtain a $(1 + ε)$-approximation to the $s-t$ distance in $G'$. We also generalize the result to a correlated setting and demonstrate experimentally that probing improves accuracy in estimating $s-t$ distances.

cs.DS↗

arXiv2024

The Geometry of Cyclical Social Trends

We investigate the emergence of periodic behavior in opinion dynamics and its underlying geometry. For this, we use a bounded-confidence model with contrarian agents in a convolution social network. This means that agents adapt their opinions by interacting with their neighbors in a time-varying social network. Being contrarian, the agents are kept from reaching consensus. This is the key feature that allows the emergence of cyclical trends. We show that the systems either converge to nonconsensual equilibrium or are attracted to periodic or quasi-periodic orbits. We bound the dimension of the attractors and the period of cyclical trends. We exhibit instances where each orbit is dense and uniformly distributed within its attractor. We also investigate the case of randomly changing social networks.

cs.MA↗

arXiv2023

2-Colorable Perfect Matching is NP-complete in 2-Connected 3-Regular Planar Graphs

The 2-colorable perfect matching problem asks whether a graph can be colored with two colors so that each node has exactly one neighbor with the same color as itself. We prove that this problem is NP-complete, even when restricted to 2-connected 3-regular planar graphs. In 1978, Schaefer proved that this problem is NP-complete in general graphs, and claimed without proof that the same result holds when restricted to 3-regular planar graphs. Thus we fill in the missing proof of this claim, while simultaneously strengthening to 2-connected graphs (which implies existence of a perfect matching). We also prove NP-completeness of $k$-colorable perfect matching, for any fixed $k \geq 2$.

cs.CC↗

arXiv2023

Unfolding Orthotubes with a Dual Hamiltonian Path

An orthotube consists of orthogonal boxes (e.g., unit cubes) glued face-to-face to form a path. In 1998, Biedl et al. showed that every orthotube has a grid unfolding: a cutting along edges of the boxes so that the surface unfolds into a connected planar shape without overlap. We give a new algorithmic grid unfolding of orthotubes with the additional property that the rectangular faces are attached in a single path -- a Hamiltonian path on the rectangular faces of the orthotube surface.

cs.CG↗

arXiv2022

Quick Relaxation in Collective Motion

We establish sufficient conditions for the quick relaxation to kinetic equilibrium in the classic Vicsek-Cucker-Smale model of bird flocking. The convergence time is polynomial in the number of birds as long as the number of flocks remains bounded. This new result relies on two key ingredients: exploiting the convex geometry of embedded averaging systems; and deriving new bounds on the s-energy of disconnected agreement systems. We also apply our techniques to bound the relaxation time of certain pattern-formation robotic systems investigated by Sugihara and Suzuki.

cs.MA↗