# Rounded Dynamic Programming for Tree-Structured Stochastic Network Design

Xiaojian Wu, Daniel Sheldon, and Shlomo Zilberstein.
Rounded Dynamic Programming for Tree-Structured Stochastic Network Design.
*Proceedings of the Twenty-Eighth Conference on Artificial
Intelligence* (AAAI), 479-485, Quebec City, Canada, 2014.

## Abstract

We develop a fast approximation algorithm called rounded dynamic programming (RDP) for stochastic network design problems on directed trees. The underlying model describes phenomena that spread away from the root of a tree, for example, the spread of influence in a hierarchical organization or fish in a river network. Actions can be taken to intervene in the network—for some cost—to increase the probability of propagation along an edge. Our algorithm selects a set of actions to maximize the overall spread in the network under a limited budget. We prove that the algorithm is a fully polynomial-time approximation scheme (FPTAS), that is, it finds (1−ε)-optimal solutions in time polynomial in the input size and 1/ε. We apply the algorithm to the problem of allocating funds efficiently to remove barriers in a river network so fish can reach greater portions of their native range. Our experiments show that the algorithm is able to produce near-optimal solutions much faster than an existing technique.

### Bibtex entry:

@inproceedings{WSZaaai14, author = {Xiaojian Wu and Daniel Sheldon and Shlomo Zilberstein}, title = {Rounded Dynamic Programming for Tree-Structured Stochastic Network Design}, booktitle = {Proceedings of the Twenty-Eighth Conference on Artificial Intelligence}, year = {2014}, pages = {479-485}, address = {Quebec City, Canada}, url = {http://rbr.cs.umass.edu/shlomo/papers/WSZaaai14.html} }shlomo@cs.umass.edu