On the Approximability of DAG Edge Deletion

Nathan Klein, Oberlin CollegeFollow

Location

King Building 341

Document Type

Presentation

Start Date

4-29-2016 4:00 PM

End Date

4-29-2016 5:15 PM

Abstract

The DAG Edge Deletion problem of k, or DED(k), is to delete the minimum weight set of edges from a directed graph such that the remaining graph has no path of length k. It can be used to find the best schedule for completing tasks with soft precedence constraints within k time-steps. In 2015 Kenkre et al. showed that DED(k) has no polynomial-time approximation algorithm with ratio better than k/2 unless the Unique Games Conjecture is false. However, the best known approximation algorithm has a ratio of k. In this work we tighten this gap by giving a (2/3)k +O(1) approximation for DED(k).

Notes

Session III, Panel 16 - On Surfaces and Edges: Using Numbers to Make Sense of Sound, Time, and Patterns
Moderator: Bob Geitz, Associate Professor of Computer Science

Major

Cello Performance; Computer Science

Advisor(s)

Amir Eldan, Cello
Alexa Sharp, Computer Science

Project Mentor(s)

Tom Wexler, Computer Science

April 2016

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Apr 29th, 4:00 PM Apr 29th, 5:15 PM

On the Approximability of DAG Edge Deletion

King Building 341

The DAG Edge Deletion problem of k, or DED(k), is to delete the minimum weight set of edges from a directed graph such that the remaining graph has no path of length k. It can be used to find the best schedule for completing tasks with soft precedence constraints within k time-steps. In 2015 Kenkre et al. showed that DED(k) has no polynomial-time approximation algorithm with ratio better than k/2 unless the Unique Games Conjecture is false. However, the best known approximation algorithm has a ratio of k. In this work we tighten this gap by giving a (2/3)k +O(1) approximation for DED(k).