1 research outputs found
Shortest-Path-Preserving Rounding
Various applications of graphs, in particular applications related to finding
shortest paths, naturally get inputs with real weights on the edges. However,
for algorithmic or visualization reasons, inputs with integer weights would
often be preferable or even required. This raises the following question: given
an undirected graph with non-negative real weights on the edges and an error
threshold , how efficiently can we decide whether we can round all
weights such that shortest paths are maintained, and the change of weight of
each shortest path is less than ? So far, only for path-shaped
graphs a polynomial-time algorithm was known. In this paper we prove, by
reduction from 3-SAT, that, in general, the problem is NP-hard. However, if the
graph is a tree with vertices, the problem can be solved in time.Comment: 20 pages, 5 figures, pre-print of an article presented at IWOCA 201