Complexity and Algorithms in Graphs

Graphs are one of the most natural mathematical structures for modeling relationships—between cities, data points, genes, or transistors—and a central question in computer science is how efficiently problems defined on them can be solved. Researchers here work at the intersection of algorithm design and mathematical theory, asking not just how to find good solutions to problems like network flow, scheduling, or clustering, but how to characterize the fundamental limits of what any algorithm can accomplish. Approximation algorithms and complexity theory together map out this landscape: when exact answers are too costly, how close can we get, and can we prove that doing better is impossible? Active open directions include tightening the gap between upper and lower bounds for problems involving submodular optimization, advancing the theory of communication complexity to better understand distributed computation, and resolving longstanding questions about the true computational cost of matrix multiplication.

Works

37,807

Total citations

534,994

Keywords

Combinatorial OptimizationApproximation AlgorithmsComplexity TheoryGraph AlgorithmsSubmodular FunctionsNetwork Flows