Complexity and Algorithms for the Discrete Fr\'echet Distance Upper Bound with Imprecise Input

We study the problem of computing the upper bound of the discrete Fr\'{e}chet distance for imprecise input, and prove that the problem is NP-hard. This solves an open problem posed in 2010 by Ahn \emph{et al}. If shortcuts are allowed, we show that the upper bound of the discrete Fr\'{e}chet distance with shortcuts for imprecise input can be computed in polynomial time and we present several efficient algorithms.Comment: 15 pages, 8 figure

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

JGraphT -- A Java library for graph data structures and algorithms

Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze and query graphs are crucial in an era where large-scale spatial, societal and economic network data are abundantly available. One such package is JGraphT, a programming library which contains very efficient and generic graph data-structures along with a large collection of state-of-the-art algorithms. The library is written in Java with stability, interoperability and performance in mind. A distinctive feature of this library is the ability to model vertices and edges as arbitrary objects, thereby permitting natural representations of many common networks including transportation, social and biological networks. Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism; matching and flow problems; approximation algorithms for NP-hard problems such as independent set and TSP; and several more exotic algorithms such as Berge graph detection. Due to its versatility and generic design, JGraphT is currently used in large-scale commercial, non-commercial and academic research projects. In this work we describe in detail the design and underlying structure of the library, and discuss its most important features and algorithms. A computational study is conducted to evaluate the performance of JGraphT versus a number of similar libraries. Experiments on a large number of graphs over a variety of popular algorithms show that JGraphT is highly competitive with other established libraries such as NetworkX or the BGL.Comment: Major Revisio

Computational Complexity for Physicists

These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.Comment: references updated, reprint available from http://itp.nat.uni-magdeburg.de/~mertens/papers/complexity.shtm