# On the Approximability of DAG Edge Deletion

## 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).

## Recommended Citation

Klein, Nathan, "On the Approximability of DAG Edge Deletion" (04/29/16). *Senior Symposium*. 28.

https://digitalcommons.oberlin.edu/seniorsymp/2016/presentations/28

## Major

Cello Performance; Computer Science

## Advisor(s)

Amir Eldan, Cello

Alexa Sharp, Computer Science

## Project Mentor(s)

Tom Wexler, Computer Science

April 2016

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).

## 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