Want to study AI or Chinese cuisine for free? Seoul expands program - The Korea Herald
Want to study AI or Chinese cuisine for free? Seoul expands program The Korea Herald
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Online Graph Coloring for $k$-Colorable Graphs
arXiv:2511.16100v2 Announce Type: replace Abstract: We study the problem of online graph coloring for $k$-colorable graphs. The best previously known deterministic algorithm uses $\widetilde{O}(n^{1-\frac{1}{k!}})$ colors for general $k$ and $\widetilde{O}(n^{5/6})$ colors for $k = 4$, both given by Kierstead in 1998. In this paper, we finally break this barrier, achieving the first major improvement in nearly three decades. Our results are summarized as follows: (1) $k \geq 5$ case. We provide a deterministic online algorithm to color $k$-colorable graphs with $\widetilde{O}(n^{1-\frac{1}{k(k-1)/2}})$ colors, significantly improving the current upper bound of $\widetilde{O}(n^{1-\frac{1}{k!}})$ colors. Our algorithm also matches the best-known bound for $k = 4$ ($\widetilde{O}(n^{5/6})$ c
Zero-Freeness of the Hard-Core Model with Bounded Connective Constant
arXiv:2604.02746v1 Announce Type: cross Abstract: We study the zero-free regions of the partition function of the hard-core model on finite graphs and their implications for the analyticity of the free energy on infinite lattices. Classically, zero-freeness results have been established up to the tree uniqueness threshold $\lambda_c(\Delta-1)$ determined by the maximum degree $\Delta$. However, for many graph classes, such as regular lattices, the connective constant $\sigma$ provides a more precise measure of structural complexity than the maximum degree. While recent approximation algorithms based on correlation decay and Markov chain Monte Carlo have successfully exploited the connective constant to improve the threshold to $\lambda_c(\sigma)$, analogous results for complex zero-freenes
Engineering Algorithms for Dynamic Greedy Set Cover
arXiv:2604.03152v1 Announce Type: new Abstract: In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade has seen significant theoretical breakthroughs for this problem, a notable gap remains between theoretical design and practical performance, as no comprehensive experimental study currently exists to validate these results. In this paper, we bridge this gap by implementing and evaluating four greedy-based dynamic algorithms across a diverse range of real-world instances. We derive our implementations from state-of-the-art frameworks (such as GKKP, STOC 2017; SU, STOC 2023; SUZ, FOCS 2024), which we simplify
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AirAsia X hikes ticket prices by 40%, cut capacity by 10% as Iran war hits fuel costs
Southeast Asia’s largest low-cost carrier AirAsia X said on Monday it was raising ticket prices by as much as 40 per cent and cutting routes to cushion the impact of the war on Iran, but stressed demand for flights remained high. The Malaysia-based no-frills airline said about 10 per cent of its overall flights had been cut so far. It has raised fuel surcharges by about 20 per cent, while fare prices have increased between 31 per cent and 40 per cent. Average jet fuel costs have soared to about...
Engineering Algorithms for Dynamic Greedy Set Cover
arXiv:2604.03152v1 Announce Type: new Abstract: In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade has seen significant theoretical breakthroughs for this problem, a notable gap remains between theoretical design and practical performance, as no comprehensive experimental study currently exists to validate these results. In this paper, we bridge this gap by implementing and evaluating four greedy-based dynamic algorithms across a diverse range of real-world instances. We derive our implementations from state-of-the-art frameworks (such as GKKP, STOC 2017; SU, STOC 2023; SUZ, FOCS 2024), which we simplify
Online Drone Coverage of Targets on a Line
arXiv:2604.02491v1 Announce Type: new Abstract: We study a problem of online targets coverage by a drone or a sensor that is equipped with a camera or an antenna of fixed half-angle of view $\alpha$. The targets to be monitored appear at arbitrary positions on a line barrier in an online manner. When a new target appears, the drone has to move to a location that covers the newly arrived target, as well as already existing targets. The objective is to design a coverage algorithm that optimizes the total length of the drone's trajectory. Our results are reported in terms of an algorithm's competitive ratio, i.e., the worst-case ratio (over all inputs) of its cost to that of an optimal offline algorithm. In terms of upper bounds, we present three online algorithms and prove bounds on their co
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