1,201 research outputs found
Maximum st-flow in directed planar graphs via shortest paths
Minimum cuts have been closely related to shortest paths in planar graphs via
planar duality - so long as the graphs are undirected. Even maximum flows are
closely related to shortest paths for the same reason - so long as the source
and the sink are on a common face. In this paper, we give a correspondence
between maximum flows and shortest paths via duality in directed planar graphs
with no constraints on the source and sink. We believe this a promising avenue
for developing algorithms that are more practical than the current
asymptotically best algorithms for maximum st-flow.Comment: 20 pages, 4 figures. Short version to be published in proceedings of
IWOCA'1
The Knapsack Problem with Neighbour Constraints
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.Comment: Full version of IWOCA 2011 pape
- …