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 settles the complexity of three sketching problems in graphs and distributions.

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

This paper presents an algorithm to generate snake-like polyominoes within a given rectangle and provides exact formulas for the maximal area of such polyominoes for certain dimensions.

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…

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.

This paper characterizes the graph structure, including cycle and path lengths, of Chebyshev permutation polynomials over the ring $\mathbb{Z}_{2^{k_1}3^{k_2}}$, demonstrating strong regularities desp…

This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.

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…

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.

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

The paper proposes Latent Geometric Chords (LGC) and LGC-H, a novel method that navigates decision boundaries using curvature-aware geometric search within a semantic manifold to generate high-fidelit…

The paper systematically explores a vast design space of cryptographic Boolean networks by formalizing six structural constraints, finding that optimal designs result from sparse, mutually compatible…

This paper provides an explicit cost analysis of Toom-4 multiplication specifically tailored for the incomplete Number Theoretic Transform (NTT) framework, offering a concrete cost model for hybrid la…

The paper presents the first general mechanism for counting arbitrary acyclic graph patterns under Local Differential Privacy (LDP), addressing challenges in pattern construction and node duplication.

The paper analyzes a fragment of Higher-Order Datalog, showing that restricting recursion to a linear form shifts its expressive power from time complexity to space complexity, specifically capturing…