On the Continuous Fermat-Weber Problem
نویسندگان
چکیده
We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the “continuous k-median (Fermat-Weber) problem” where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed as an integral over the relevant region, versus the usual discrete sum of distances. The resulting facility location problems are inherently geometric, requiring analysis techniques of computational geometry. We provide polynomial-time algorithms for various versions of the L1 1-median (Fermat-Weber) problem. We also consider the multiple-center version of the L1 k-median problem, which we prove is NP-hard for large k. MSC Classification: 90B85, 68U05 ACM Classification: F.2.2
منابع مشابه
On the continuous Fermat-Weber problem for a convex polygon using Euclidean distance
In this paper, we consider the continuous Fermat-Weber problem, where the customers are continuously (uniformly) distributed along the boundary of a convex polygon. We derive the closed-form expression for finding the average distance from a given point to the continuously distributed customers along the boundary. A Weiszfeld-type procedure is proposed for this model, which is shown to be linea...
متن کاملar X iv : c s . C G / 0 31 00 27 v 1 1 5 O ct 2 00 3 On the Continuous Fermat - Weber Problem ∗
We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the “continuous k-median (Fermat-Weber) problem” where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed a...
متن کاملar X iv : c s / 03 10 02 7 v 1 [ cs . C G ] 1 5 O ct 2 00 3 On the Continuous Fermat - Weber Problem ∗ Sándor
We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the “continuous k-median (Fermat-Weber) problem” where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed a...
متن کاملAdaptation of the Probability Changing Method for Weber Problem with an Arbitrary Metric
Fermat-Weber problem in its simple form (unconstrained, single facility, Euclidean metric) is well investigated. Lot of algorithms are also developed for more complicated cases. But the generalized multi-facility problem with barriers, restricted zones and an arbitrary metric has no well-known algorithm for its solving. In this paper, we consider the planar multi-facility Weber problem with res...
متن کاملOn Newton's Method for the Fermat-Weber Location Problem
This paper considers the Fermat-Weber location problem. It is shown that, after a suitable initialization, the standard Newton method can be applied to the Fermat-Weber problem and is globally and locally quadratically convergent. A numerical comparison with the popular Weiszfeld algorithm shows that Newton’s method is significantly more efficient than the Weiszfeld scheme.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Operations Research
دوره 53 شماره
صفحات -
تاریخ انتشار 2005