Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, May 12, 2022, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Hung Hoang

Hardness of Approximating the Rank of a Graph Divisor

Graph divisor theory is a combinatorial analogue of the divisor theory in algebraic geometry. A fundamental concept in this area is the rank of a graph divisor. It is already known that computing the rank is NP-hard (Kiss and Tóthmérész, 2015). By a reduction from the Minimum Target Set Selection problem, we show that no polynomial-time algorithm can approximate the rank within the factor of 2^{O(log^{1-ε}n)} unless P = NP, and assuming a weaker conjecture (the Planted Dense Subgraph Conjecture), there is no polynomial time O(n^{1/2-ε})-approximation

Joint work with Kristóf Bérczi and Lilla Tóthmérész.

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