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

Date and Time: Thursday, February 14, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Matthias Mnich (Universitaet des Saarlandes)

Max-Cut Parameterized above the Edwards-Erdos Bound

We study the boundary of tractability for the Max-Cut problem in graphs. Our main result shows that Max-Cut above the Edwards-Erdos bound is fixed-parameter tractable: we give an algorithm that for any connected graph with n vertices and m edges finds a cut of size m/2 + (n−1)/4 + k in time 8^k * O(n⁴), or decides that no such cut exists.

This answers a long-standing open question from parameterized complexity that has been posed a number of times over the past 15 years.

Our algorithm is asymptotically optimal, under the Exponential Time Hypothesis, and is strengthened by a polynomial-time computable kernel of polynomial size.

This work appeared at ICALP 2012, and is joint with Robert Crowston and Mark Jones from Royal Holloway.

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