On the Number of Iterations for Dantzig-Wolfe Optimization and Packing-Covering Approximation Algorithms

We give a lower bound on the iteration complexity of a natural class of Lagrangean-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$ variables, with high probability, any such algorithm requires $\Omega(\rho \log(m)/\epsilon^2)$ iterations to compute a $(1+\epsilon)$-approximate solution, where $\rho$ is the width of the input. The bound is tight for a range of the parameters $(m,n,\rho,\epsilon)$. The algorithms in the class include Dantzig-Wolfe decomposition, Benders' decomposition, Lagrangean relaxation as developed by Held and Karp [1971] for lower-bounding TSP, and many others (e.g. by Plotkin, Shmoys, and Tardos [1988] and Grigoriadis and Khachiyan [1996]). To prove the bound, we use a discrepancy argument to show an analogous lower bound on the support size of $(1+\epsilon)$-approximate mixed strategies for random two-player zero-sum 0/1-matrix games

Multicast Mobility in Mobile IP Version 6 (MIPv6) : Problem Statement and Brief Survey

Publisher PD

QuLa: service selection and forwarding table population in service-centric networking using real-life topologies

The amount of services located in the network has drastically increased over the last decade which is why more and more datacenters are located at the network edge, closer to the users. In the current Internet it is up to the client to select a destination using a resolution service (Domain Name System, Content Delivery Networks ...). In the last few years, research on Information-Centric Networking (ICN) suggests to put this selection responsibility at the network components; routers find the closest copy of a content object using the content name as input. We extend the principle of ICN to services; service routers forward requests to service instances located in datacenters spread across the network edge. To solve this problem, we first present a service selection algorithm based on both server and network metrics. Next, we describe a method to reduce the state required in service routers while minimizing the performance loss caused by this data reduction. Simulation results based on real-life networks show that we are able to find a near-optimal load distribution with only minimal state required in the service routers

On the Benefit of Virtualization: Strategies for Flexible Server Allocation

Virtualization technology facilitates a dynamic, demand-driven allocation and migration of servers. This paper studies how the flexibility offered by network virtualization can be used to improve Quality-of-Service parameters such as latency, while taking into account allocation costs. A generic use case is considered where both the overall demand issued for a certain service (for example, an SAP application in the cloud, or a gaming application) as well as the origins of the requests change over time (e.g., due to time zone effects or due to user mobility), and we present online and optimal offline strategies to compute the number and location of the servers implementing this service. These algorithms also allow us to study the fundamental benefits of dynamic resource allocation compared to static systems. Our simulation results confirm our expectations that the gain of flexible server allocation is particularly high in scenarios with moderate dynamics

Applying a Genetic Algorithm to a m-TSP: Case Study of a Decision Support System for Optimizing a Beverage Logistics Vehicles Routing Problem

Route optimization has become an increasing problem in the transportation and logistics sector within the development of smart cities. This article aims to demonstrate the implementation of a genetic algorithm adapted to a Vehicle Route Problem (VRP) in a company based in the city of Covilhã (Portugal). Basing the entire approach to this problem on the characteristic assumptions of the Multiple Traveling Salesman Problem (m-TSP) approach, an optimization of the daily routes for the workers assigned to distribution, divided into three zones: North, South and Central, was performed. A critical approach to the returned routes based on the adaptation to the geography of the Zones was performed. From a comparison with the data provided by the company, it is predicted by the application of a genetic algorithm to the m-TSP, that there will be a reduction of 618 km per week of the total distance traveled. This result has a huge impact in several forms: clients are visited in time, promoting provider-client relations; reduction of the fixed costs with fuel; promotion of environmental sustainability by the reduction of logistic routes. All these improvements and optimizations can be thought of as contributions to foster smart cities.Fundação para a Ciência e a Tecnologia (FCT—MCTES) for its financial support via the project UIDB/00151/2020 (C-MAST).info:eu-repo/semantics/publishedVersio