A seminal result of Koml & oacute;s, S & aacute;rk & ouml;zy, and Szemer & eacute;di states that any $n$ -vertex graph $G$ with minimum degree at least $(1/2+\alpha )n$ contains every $n$ -vertex tree $T$ of bounded degree. Recently, Pham, Sah, Sawhney, and Simkin extended this result to show that such graphs $G$ in fact support an optimally spread distribution on copies of a given $T$ , which implies, using the recent breakthroughs on the Kahn-Kalai conjecture, the robustness result that $T$ is a subgraph of sparse random subgraphs of $G$ as well. Pham, Sah, Sawhney, and Simkin construct their optimally spread distribution by following closely the original proof of the Koml & oacute;s-S & aacute;rk & ouml;zy-Szemer & eacute;di theorem which uses the blow-up lemma and the Szemer & eacute;di regularity lemma. We give an alternative, regularity-free construction that instead uses the Koml & oacute;s-S & aacute;rk & ouml;zy-Szemer & eacute;di theorem (which has a regularity-free proof due to Kathapurkar and Montgomery) as a black box. Our proof is based on the simple and general insight that, if $G$ has linear minimum degree, almost all constant-sized subgraphs of $G$ inherit the same minimum degree condition that $G$ has.
Many approaches to program synthesis perform a combinatorial search within a large space of programs to find one that satisfies a given specification. To tame the search space blowup, previous works introduced probabilistic and neural approaches to guide this combinatorial search by inducing heuristic cost functions. Best-first search algorithms ensure to search in the exact order induced by the cost function, significantly reducing the portion of the program space to be explored. We present a new best-first search algorithm called Eco Search, which is the first no-delay algorithm for pre-generation cost function: the amount of compute required between outputting two programs is constant, and in particular does not increase over time. This key property yields important speedups: we observe that Eco Search outperforms its predecessors on two classical domains.
Developing countries face a growing demand for video analytics, yet often lack sufficient computational resources. This paper addresses this challenge by proposing and evaluating optimization techniques for efficient video stream processing on resource-constrained devices, including edge systems. We introduce and evaluate several techniques, including image resizing, frame skipping, parallel processing, threading, queue management, memory optimization, and buffering. Experimental results demonstrate substantial improvements in frames per second (FPS) and memory usage, enabling real-time video analytics without compromising accuracy namely in object detection. By effectively balancing performance and resource consumption, our methods facilitate the deployment of advanced AI-driven video analysis in resource-limited environments, paving the way for practical real-time monitoring and alert systems.
