Sorting under Forbidden Comparisons

In this paper we study the problem of sorting under forbidden comparisons where some pairs of elements may not be compared (forbidden pairs). Along with the set of elements V the input to our problem is a graph G(V, E), whose edges represents the pairs that we can compare in constant time. Given a graph with n vertices and m =(n2) - q edges we propose the first non-trivial deterministic algorithm which makes O((q + n) log n) comparisons with a total complexity of O(n2 + qω/2), where ω is the exponent in the complexity of matrix multiplication. We also propose a simple randomized algorithm for the problem which makes Õ(n2/√q + n+n√q) probes with high probability. When the input graph is random we show that Õ(min (n3/2, pn2)) probes suffice, where p is the edge probability

Sorting Under Forbidden Comparisons

In this paper we study the problem of sorting under forbidden comparisons where some pairs of elements may not be compared (forbidden pairs). Along with the set of elements V the input to our problem is a graph G(V, E), whose edges represents the pairs that we can compare in constant time. Given a graph with n vertices and m = binom(n)(2) - q edges we propose the first non-trivial deterministic algorithm which makes O((q + n)*log(n)) comparisons with a total complexity of O(n^2 + q^(omega/2)), where omega is the exponent in the complexity of matrix multiplication. We also propose a simple randomized algorithm for the problem which makes widetilde O(n^2/sqrt(q+n) + nsqrt(q)) probes with high probability. When the input graph is random we show that widetilde O(min(n^(3/2), pn^2)) probes suffice, where p is the edge probability

The balanced 2-median and 2-maxian problems on a tree

This paper deals with the facility location problems with balancing on allocation clients to servers. Two bi-objective models are considered, in which one objective is the traditional p-median or p-maxian objective and the second is to minimize the maximum demand volume allocated to any facility. An edge deletion method with time complexity O(n^2) is presented for the balanced $2$-median problem on a tree. For the balanced 2-maxian problem, it is shown the optimal solution is two end vertices of the diameter of the tree, which can be obtained in a linear time.Comment: 19 page

Grid Facilities Design: Dynamic Modular Deployment of Production, Handling and Storage Resources

To survive and thrive in a fast-moving environment, facilities must be designed to show adaptability, flexibility and robustness. As some facilities are depicted by heavy and sophisticated equipment costly and hard to displace, others are composed of moveable workstations with highly flexible workers. In most cases, the trade-off is between the cost of redeploying the resources and the excessive cost of material handling and storage incurred by an inefficient deployment of the resources. We propose a design strategy based on (1) conceiving and designing the facility as a stable grid of modules, (2) dynamically deploying production, storage and handling resources to these modules, and (3) dynamically assigning process-product combinations to the modules so as to meet stochastic and dynamically evolving product demand on a rolling planning horizon. We illustrate the strategy as applied to a computer refurbishing and recycling facility

A Scalable Algorithm for Locating Distribution Centers on Real Road Networks

The median problem is a type of network location problem that aims at finding a node with the total minimum demand weighted distance to a set of demand nodes in a weighted graph. In this research, an algorithm for solving the median problem on real road networks is proposed. The proposed algorithm, referred to as the multi-threaded Dijkstra’s (MTD) algorithm, is then used to optimally locate Wal-Mart distribution centers on the 28-million node road network of the United States with the objective of minimizing the total demand weighted transportation cost. The resulting optimal location configuration of Wal-Mart distribution centers improves the total transportation cost by 40%

A SOLUTION ALGORITHM FOR p-MEDIAN LOCATION PROBLEM ON UNCERTAIN RANDOM NETWORKS

This paper investigatesthe classical $p$-median location problem in a network in which some of the vertex weights and the distances between vertices are uncertain and while others are random. For solving the $p$-median problem in an uncertain random network, an optimization model based on the chance theory is proposed first and then an algorithm is presented to find the $p$-median. Finally, a numerical example is given to illustrate the efficiency of the proposed metho