Combinatorial Algorithms

Volume 7056 of the series Lecture Notes in Computer Science pp 71-84

The 1-Neighbour Knapsack Problem

  • Glencora BorradaileAffiliated withOregon State University
  • , Brent HeeringaAffiliated withWilliams College
  • , Gordon WilfongAffiliated withBell Labs

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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.