The 1-neighbour knapsack problem

Authors:
Glencora Borradaile;Brent Heeringa;Gordon Wilfong
Affiliations:
Oregon State University, United States;Williams College, United Kingdom;Bell Labs, United States
Venue:
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Year:
2011

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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. 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.