Tootfinder

Detours In Graphs
Frank Bullock
https://arxiv.org/abs/2507.12086 https://arxiv.org/pdf/2507.12086

Detours In Graphs
A detour in a graph is a longest path. This thesis is mainly about connected, non-traceable graphs with the property that each vertex is the start (or end) vertex of a detour. There are also related results on claw-free, 2-connected, non-traceable graphs, and maximal non-traceable graphs.

LLM-Based Instance-Driven Heuristic Bias In the Context of a Biased Random Key Genetic Algorithm
Camilo Chac\'on Sartori, Mart\'in Isla Pino, Pedro Pinacho-Davidson, Christian Blum
https://arxiv.org/abs/2509.09707

LLM-Based Instance-Driven Heuristic Bias In the Context of a Biased Random Key Genetic Algorithm
Integrating Large Language Models (LLMs) within metaheuristics opens a novel path for solving complex combinatorial optimization problems. While most existing approaches leverage LLMs for code generation to create or refine specific heuristics, they often overlook the structural properties of individual problem instances. In this work, we introduce a novel framework that integrates LLMs with a Biased Random-Key Genetic Algorithm (BRKGA) to solve the NP-hard Longest Run Subsequence problem. Our …

Yesterday near Rossgundscharte, Allgäu High Alps
(Longest, most stunning & varied tour in a while, traversing Warmatsgundtal into Rappenalptal, Germany's southernmost valley — 21km, incl. 1450 hm grueling descent over loose gravel...)
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