Search results for "Triangle inequality"
showing 5 items of 5 documents
The facility location problem with capacity transfers
2020
Abstract This paper explores the concept of capacity transfer in the context of capacitated facility location problems. This is accomplished by assuming that facilities with surplus capacity/production can cooperate with those facing shortage by transferring part of that capacity/production. Such a transfer incurs a cost that nonetheless may be compensated by savings both in the installation costs and in the distribution costs. Mixed-integer mathematical programming models are proposed for the problem. A distinction is made between the case in which the triangle inequality holds for the transfer costs and the case in which it does not. We present compact models, which are enhanced with vali…
On the metric properties of dynamic time warping
1987
Recently, some new and promising methods have been proposed to reduce the number of Dynamic Time Warping (DTW) computations in Isolated Word Recognition. For these methods to be properly applicable, the verification of the Triangle Inequality (TI) by the DTW-based Dissimilarity Measure utilized seems to be an important prerequisite.
Order-distance and other metric-like functions on jointly distributed random variables
2013
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in dealing with the problem of selective probabilistic causality encountered in behavioral sciences and in quantum physics. The problem reduces to that of ascertaining the existence of a joint distribution for a set of variables with known distributions of certain subsets of this set. Any violation of the triangle inequality or its consequences by one of our functions when applied to such a set rules out the existence of this joint distribution. We focus on…
Bidirectional labeling in column-generation algorithms for pickup-and-delivery problems
2018
Abstract For the exact solution of many types of vehicle-routing problems, column-generation based algorithms have become predominant. The column-generation subproblems are then variants of the shortest-path problem with resource constraints which can be solved well with dynamic-programming labeling algorithms. For vehicle-routing problems with a pickup-and-delivery structure, the strongest known dominance between two labels requires the delivery triangle inequality (DTI) for reduced costs to hold. When the direction of labeling is altered from forward labeling to backward labeling, the DTI requirement becomes the pickup triangle inequality (PTI). DTI and PTI cannot be guaranteed at the sam…