Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Modelling financial markets using methods from network theory.

This thesis discusses how properties of complex network theory can be used to study financial time series, in particular time series for stocks on the DAX 30. First, we make a comparison between three correlation-based networks: minimum spanning trees; assets graphs and planar maximally filtered graphs. A series of each of these network types is created for the same dataset of time series' of DAX 30 stocks and we consider what information each network can provide about the relationship between the stock prices from the underlying time series. We also analyse two specific time periods in further detail - a period of crisis and a period of recovery for the German economy. Next, we look at the structure and representations of planar maximally filtered graphs and in particular we consider the vertices that form the 3-cliques and 4-cliques [Tumminello et al. (2005)] state '...normalizing quantities are n_s - 3 for 4-cliques and 3n_s - 8 for 3-cliques. Although we lack a formal proof, our investigations suggest that these numbers are the maximal number of 4-cliques and 3-cliques, respectively, that can be observed in a PMFG of n_s elements.' Within this thesis we provide a proof for these quantities and a different construction algorithm. Finally, rather than correlation-based networks, we discuss two relatively new types of networks: visibility graphs and the geometrically simpler horizontal visibility graphs. We review the field's that these networks have already been applied to and consider if this is an appropriate method to apply to financial time series - specifically stock prices. We also consider using horizontal visibility graphs as a method for distinguishing between random and chaotic series within stock price time series

Approximation and online algorithms in scheduling and coloring

In the last three decades, approximation and online algorithms have become a major area of theoretical computer science and discrete mathematics. Scheduling and coloring problems are among the most popular ones for which approximation and online algorithms have been analyzed. On one hand, motivated by the well-known difficulty to obtain good lower bounds for the problems, it is particularly hard to prove results on the online and offline performance of algorithms. On the other hand, the theoretically oriented studies of approximation and online algorithms for scheduling and coloring have also impact on the development of better algorithms for real world applications. In the thesis we present approximation algorithms and online algorithms for a number of scheduling and labeling (coloring) problems. Our work in the first part of the thesis is devoted to scheduling problems with the average weighted completion time objective function, that is primarily motivated by some theoretical questions which were open for a number of recent years. Here we present a general method which leads to the design of polynomial time approximation schemes (PTASs), best possible approximation results. In contrast, our work in the second part of the thesis is motivated by practical applications. We consider a number of new labeling and scheduling problems which occur in the design of communication networks. Here we present and analyze efficient approximation and online algorithms. We use very simple techniques which do not require large computational resources

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum