This paper proves that no single-pass semi-streaming algorithm can achieve a better-than-half approximation to the maximum matching problem, implying the optimality of the naive greedy algorithm.

The paper develops a new framework for proving lower bounds for the maximum matching problem in the semi-streaming model, improving upon the previous best known bounds.

A new polynomial-time algorithm is presented for optimally coloring perfect graphs using graph-theoretic operations and iterative walk counting.

This paper introduces a streaming model with catalytic memory and shows dramatic space savings for data stream algorithms, providing exact computation of frequency moments using multi-pass algorithms…

This paper proposes two algorithms for approximating the number of four-cycles in graph edge streams, improving upon existing theoretical bounds and handling non-concentrated four-cycles in one-pass.

The authors map the problem of finding the maximum cut of a planar graph with arbitrary weights to a minimum T-join problem in the absolute dual graph, enabling the use of shortest paths and adapting…

This paper presents an optimized algorithm for computing cut sets of a path set in graph theory and introduces a vectorized computational framework for property calculations.

This paper presents deterministic and randomized algorithms for the incremental dominating set problem in vertex-weighted graphs, achieving competitive ratios of O(Δ) and O(log^2Δ) respectively. It al…

This paper studies the triangle-densest-$k$-subgraph problem in an average-case model and proposes spectral and semidefinite algorithms for its recovery.

The paper shows that every problem asking if a given graph has an edge-coloring without an edge-colored clique from a fixed family is poly-time equivalent to a Constraint Satisfaction Problem, resulti…

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

This paper presents new polynomial-time algorithms for determining the winner of the unbiased triangle game on the edge set of general graphs using the edge-triangle incidence graph.

This paper presents four novel parallel algorithms for maintaining a rooted spanning forest in dynamic graphs, achieving a throughput of 2 million insertions and 1.4 million deletions per second.

This paper studies the complexity of the Flood-It game on various graph classes and provides polynomial-time algorithms for Free Flood-It on graphs free of certain jewels, while proving NP-completenes…