Combinatorics

Combinatorics is a fundamental mathematical discipline that focuses on the study of discrete objects and their properties. The present workshop featured research in such diverse areas as Extremal, Probabilistic and Algebraic Combinatorics, Graph Theory, Discrete Geometry, Combinatorial Optimization, Theory of Computation and Statistical Mechanics. It provided current accounts of exciting developments and challenges in these fields and a stimulating venue for a variety of fruitful interactions. This is a report on the meeting, containing extended abstracts of the presentations and a summary of the problem session

Graph Pattern Matching on Symmetric Multiprocessor Systems

Graph-structured data can be found in nearly every aspect of today's world, be it road networks, social networks or the internet itself. From a processing perspective, finding comprehensive patterns in graph-structured data is a core processing primitive in a variety of applications, such as fraud detection, biological engineering or social graph analytics. On the hardware side, multiprocessor systems, that consist of multiple processors in a single scale-up server, are the next important wave on top of multi-core systems. In particular, symmetric multiprocessor systems (SMP) are characterized by the fact, that each processor has the same architecture, e.g. every processor is a multi-core and all multiprocessors share a common and huge main memory space. Moreover, large SMPs will feature a non-uniform memory access (NUMA), whose impact on the design of efficient data processing concepts should not be neglected. The efficient usage of SMP systems, that still increase in size, is an interesting and ongoing research topic. Current state-of-the-art architectural design principles provide different and in parts disjunct suggestions on which data should be partitioned and or how intra-process communication should be realized. In this thesis, we propose a new synthesis of four of the most well-known principles Shared Everything, Partition Serial Execution, Data Oriented Architecture and Delegation, to create the NORAD architecture, which stands for NUMA-aware DORA with Delegation. We built our research prototype called NeMeSys on top of the NORAD architecture to fully exploit the provided hardware capacities of SMPs for graph pattern matching. Being an in-memory engine, NeMeSys allows for online data ingestion as well as online query generation and processing through a terminal based user interface. Storing a graph on a NUMA system inherently requires data partitioning to cope with the mentioned NUMA effect. Hence, we need to dissect the graph into a disjunct set of partitions, which can then be stored on the individual memory domains. This thesis analyzes the capabilites of the NORAD architecture, to perform scalable graph pattern matching on SMP systems. To increase the systems performance, we further develop, integrate and evaluate suitable optimization techniques. That is, we investigate the influence of the inherent data partitioning, the interplay of messaging with and without sufficient locality information and the actual partition placement on any NUMA socket in the system. To underline the applicability of our approach, we evaluate NeMeSys against synthetic datasets and perform an end-to-end evaluation of the whole system stack on the real world knowledge graph of Wikidata

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