The Knapsack Problem with Neighbour Constraints
Data Structures and Algorithms
2011-09-28 v4 Discrete Mathematics
Abstract
We study a constrained version of the knapsack problem in which dependencies between items are given by the adjacencies of a graph. In the 1-neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also selected. In the all-neighbours knapsack problem, an item can be selected only if all its neighbours are also selected. We give approximation algorithms and hardness results when the nodes have both uniform and arbitrary weight and profit functions, and when the dependency graph is directed and undirected.
Cite
@article{arxiv.0910.0777,
title = {The Knapsack Problem with Neighbour Constraints},
author = {Glencora Borradaile and Brent Heeringa and Gordon Wilfong},
journal= {arXiv preprint arXiv:0910.0777},
year = {2011}
}
Comments
Full version of IWOCA 2011 paper