This paper introduces a new variant of the Traveling Salesman Problem where the goal is to find two paths connecting a set of sites while minimizing the Fréchet distance between the two paths.

The paper systematically studies the trade-offs between the number of slopes, bends per edge, and required area for planar drawings of bounded-degree graphs, providing new constructions for high-degre…

The paper introduces and explores Truly Linear FPT (TLFPT), a complexity class defined by $O(n) + f(k)$, demonstrating that it is a strict subset of standard Linear FPT and providing new algorithms fo…

The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…

The paper introduces a method to efficiently detect 'essential' constraints in Boolean MinCSPs, significantly reducing the search space for solving these problems and providing a dichotomy theorem for…

PlanarBench introduces a novel benchmark to test LLM spatial reasoning by requiring them to draw planar graphs as ASCII art from an edge list, finding that edge count is a stronger difficulty predicto…

This paper develops a parameterized algorithm for the NP-complete Tree Containment problem, showing it can be solved efficiently based on a structural parameter called scanwidth.

The paper provides a tight, transparent, and closed-form analysis of the trade-off function for Differentially Private SGD using random shuffling, significantly improving upon previous methods and est…

This paper introduces Electric Flow Sampling (elfs) as a zero-error quantum walk primitive and uses it to derive improved quantum algorithms for various graph problems, including semi-supervised learn…

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

This paper introduces survey sampling techniques to estimate or minimize empirical pairwise loss functions, showing that targeting informative pairs significantly reduces computational cost while main…

The paper presents two new attacks on decisional $k$-sparse LWE and LPN problems for higher moduli $q$ by generalizing the Kikuchi method using graph theory.

The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…

This paper presents an algorithmic framework for exhaustively generating and tabulating knot and link diagrams on the thickened torus.

The paper analyzes the sample complexity of contextual bandits in the $s$-sparse setting, achieving optimal sample bounds for identifying an $\epsilon$-optimal policy.

The paper introduces a novel public key encryption scheme with high security by leveraging the conjectured intractability of two types of highly corrupted constraint satisfaction problems (CSPs).

The paper proposes using Maximum Independent Set (MIS) algorithms on similarity graphs to select a maximally diverse and non-redundant subset of prompts for LLM benchmarking, achieving consistent rank…