Tootfinder

Sparse Navigable Graphs for Nearest Neighbor Search: Algorithms and Hardness
Sanjeev Khanna, Ashwin Padaki, Erik Waingarten
https://arxiv.org/abs/2507.14060

Sparse Navigable Graphs for Nearest Neighbor Search: Algorithms and Hardness
We initiate the study of approximation algorithms and computational barriers for constructing sparse $α$-navigable graphs [IX23, DGM+24], a core primitive underlying recent advances in graph-based nearest neighbor search. Given an $n$-point dataset $P$ with an associated metric $\mathsf{d}$ and a parameter $α\geq 1$, the goal is to efficiently build the sparsest graph $G=(P, E)$ that is $α$-navigable: for every distinct $s, t \in P$, there exists an edge $(s, u) \in E$ with $\mathsf{d}(u, t)…

The Pandora's Box Problem with Sequential Inspections
Ali Aouad, Jingwei Ji, Yaron Shaposhnik
https://arxiv.org/abs/2507.07508 https://

The Pandora's Box Problem with Sequential Inspections
The Pandora's box problem (Weitzman 1979) is a core model in economic theory that captures an agent's (Pandora's) search for the best alternative (box). We study an important generalization of the problem where the agent can either fully open boxes for a certain fee to reveal their exact values or partially open them at a reduced cost. This introduces a new tradeoff between information acquisition and cost efficiency. We establish a hardness result and employ an array of techniques in stochasti…