The Redei-Berge Symmetric Function of a Directed Graph
Explore symmetric functions in directed graphs, examining Redei's theorem on tournaments and Chow's path-cycle function. Discover new expansions and refinements in graph theory.
Counting Partitions by Genus
Explore set partition counting by genus, focusing on primitive partitions and functional equations to reconstruct all partitions, with emphasis on genus 0-2 cases.
NetworkX is Fast Now - Graph Analytics Unleashed
Discover NetworkX's power for graph analytics, from beginner-friendly API to accelerated backends. Learn to extract insights from data using advanced tools for scalable graph analysis.
Graphs and Vogue Dance: Using Data Structures to Create Choreographies
Explore how graph data structures can be used to create and visualize Vogue Dance choreographies, combining computer science concepts with artistic expression in this innovative approach to dance composition.
Sparsifying Set Systems for Coverage Problems
Explore recent advancements in sparsifying set systems for coverage problems, focusing on sublinear graph simplification techniques.
Improved Streaming Algorithms for Max-DICUT via Local Snapshots
Explore advanced streaming algorithms for Max-DICUT problem, focusing on local graph snapshots to surpass the 4/9 approximation in sublinear space.
Approximating Maximum Matching Requires Almost Quadratic Time
Explore algorithms for estimating maximum matching size, focusing on recent advancements and lower bounds. Gain insights into subquadratic time complexity and its limitations in graph theory.
Online Algorithms for Spectral Hypergraph Sparsification
Explore online algorithms for spectral hypergraph sparsification, focusing on space-efficient methods for handling streaming hyperedges and producing accurate sparsifiers.
On (1 + ε)-Approximate (Vertex) Cut Sparsifiers
Explore advanced graph compression techniques for planar and quasi-bipartite graphs, focusing on high-quality cut sparsifiers and their size bounds. Analyze contraction-based approaches and their limitations.
Stochastic Minimum Vertex Cover with Few Queries: A 3/2-Approximation
Explore a 3/2-approximation algorithm for stochastic vertex cover using O(n/p) non-adaptive queries, improving upon previous 2-approximation methods and discussing extensions to correlated edge realizations.
Improved Bounds for Fully Dynamic Matching via Ordered Ruzsa-Szemeredi Graphs
Explore advanced algorithms for dynamic maximum matching using Ordered Ruzsa-Szemeredi Graphs, improving update time to n^{o(1)} * ORS(n) and reducing the problem to a combinatorial bound.
New Algorithms for Directed Spanner Problems and Generalizations
Explore recent advancements in directed spanner algorithms, including online and offline settings, weighted variants, and buy-at-bulk extensions.
Dynamic Matching and Ordered Ruzsa-Szemerédi Graphs - Towards Constructive Matching Sparsifiers
Explore approaches for designing fast dynamic algorithms for approximate matchings, focusing on fully dynamic settings and the concept of matching sparsifiers in graph theory.
Maximum Matching in O(log log n) Passes in Dynamic Streams
Explore an algorithm for approximating maximum matching in dynamic streams, achieving O(1)-approximation in O(log log n) passes and O(n poly log n) space, with lower bound proof.
Planar Partition Oracles for Bounded Degree Graphs in Polynomial Time
Explore planar graph partition oracles for bounded degree graphs, focusing on hyperfinite decompositions and their applications in sublinear algorithms and property testing.
Sparsification: Graphs, CSPs and Codes - Sublinear Graph Simplification
Explore graph sparsification, CSP compression, and code sparsification techniques. Learn about cutting-edge research in sublinear graph simplification and its applications to various domains.
Toward Optimal Semi-streaming Algorithm for (1+ε)-Approximate Maximum Matching
Explore a deterministic algorithm for (1+ε)-approximate maximum matching, improving pass-complexity and advancing solutions in various computational models.
O(log log n) Passes is Optimal for Semi-Streaming Maximal Independent Set
Explore optimal passes for semi-streaming maximal independent set, focusing on O(log log n) algorithm and new lower bound proof using extremal graphs and round elimination techniques.
Subgraph Counting and Seed Counting in Graph Theory
Explore sublinear subgraph counting and sampling techniques, focusing on the advantages of counting seeds in graph analysis.
Monotonicity Testing, Routing, and the Lehman-Ron Theorem on Hypercube Properties
Explore connections between monotonicity testing, routing on hypercubes, and Lehman-Ron theorem. Gain insights into efficient property testers and low-congestion flows on directed hypercubes.
Recent Developments in Testing Bounded-Degree Graphs
Explore recent advancements in testing bounded-degree graphs, including locally-characterized expander graphs, graph isomorphism studies, and applications of robustly self-ordered graphs.