1 research outputs found
Approximation Algorithms for Route Planning with Nonlinear Objectives
We consider optimal route planning when the objective function is a general
nonlinear and non-monotonic function. Such an objective models user behavior
more accurately, for example, when a user is risk-averse, or the utility
function needs to capture a penalty for early arrival. It is known that as
nonlinearity arises, the problem becomes NP-hard and little is known about
computing optimal solutions when in addition there is no monotonicity
guarantee. We show that an approximately optimal non-simple path can be
efficiently computed under some natural constraints. In particular, we provide
a fully polynomial approximation scheme under hop constraints. Our
approximation algorithm can extend to run in pseudo-polynomial time under a
more general linear constraint that sometimes is useful. As a by-product, we
show that our algorithm can be applied to the problem of finding a path that is
most likely to be on time for a given deadline.Comment: 9 pages, 2 figures, main part of this paper is to be appear in
AAAI'1