This study proposes a bi-objective model for capacitated multi-vehicle allocation of customers to potential distribution centers (DCs).The optimization objectives are to minimize transit time and total cost including opening cost, assumed for opening potential DCs and shipping cost from DCs to the customers where considering heterogeneous vehicles lead to a more realistic model and cause more c...

This paper presents novel techniques that allow the solution to several open problems regarding embedding of finite metric spaces into Lp. We focus on proving near optimal bounds on the dimension with which arbitrary metric spaces embed into Lp. The dimension of the embedding is of very high importance in particular in applications and much effort has been invested in analyzing it. However, no ...

We consider the dynamical inverse problem for wave equation on a metric tree graph and describe Leaf Peeling (LP) method. The main step of method is recalculating response operator from original to peeled tree. LP allows us recover connectivity, potential function lengths its edges given finite time interval.

We consider approximation algorithms for the metric labeling problem. This problem was introduced in a paper by Kleinberg and Tardos [J. ACM, 49 (2002), pp. 616–630] and captures many classification problems that arise in computer vision and related fields. They gave an O(log k log log k) approximation for the general case, where k is the number of labels, and a 2-approximation for the uniform ...

In this note we study the generation of C0-semigroups by first order differential operators on Lp(R+,Cℓ)×Lp([0,1],Cm) with general boundary conditions. many cases are able to characterize property in terms invertibility a matrix associated The abstract results used well-posedness transport equations non-compact metric graphs.

We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of Lp-spaces. We use this locally finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any Lp-space into any Banach space X containing the l n p ’s. Finally using an...

We consider the problem of computing shortest paths in three-dimensions in the presence of a single-obstacle polyhedral terrain, and present a new algorithm that for any p ≥ 1, computes a (c + ε)approximation to the Lp-shortest path above a polyhedral terrain in O( ε log n log log n) time and O(n log n) space, where n is the number of vertices of the terrain, and c = 2(p−1)/p. This leads to a F...