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

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 presents a novel and significantly faster algorithm for computing the second discrete homology group of a graph by identifying five basic quotient shapes of the 3-cube.

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 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.

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

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 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 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 proposes a scalable topological learning framework for higher-order graph representation by introducing simplified and factored cellular Weisfeiler Leman tests and a novel random walk metho…

The paper introduces a hybrid WGAN-GA framework that uses a Genetic Algorithm (GA) to refine graphs generated by a GAN, significantly reducing structural deviations and improving realism.

This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.

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

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…

The paper introduces GraphARC, a new benchmark for abstract reasoning on graph-structured data, demonstrating that current state-of-the-art language models struggle with full graph transformation task…

The paper introduces Graph Cascades, a mesoscopic rewiring technique that enhances Graph Neural Networks by promoting node pairs with strong multi-hop connections to direct edges, improving performanc…

The paper introduces 'bridges,' a type of morphism between encryption schemes, and provides a general recipe for constructing them, showing that their security relies on the security of the initial sc…

The paper introduces a diffusion-based uncertainty model for robust optimization on graphs, showing that the resulting computational complexity depends critically on the interaction between the uncert…