Incremental Maintenance of Maximal Cliques in a Dynamic Graph

We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as the first change-sensitive algorithms for clique maintenance, whose runtime is proportional to the magnitude of the change in the set of maximal cliques. We present experimental results showing these algorithms are efficient in practice and are faster than prior work by two to three orders of magnitude.Comment: 18 pages, 8 figure

Graph Data Processing and Analysis: From Algorithms to System Development

There are many real-world application domains where data can be naturally modelled as graphs, such as social networks and computer networks. The amount of data generated and published is rapidly increasing with the explosion of information. Effective storage of graph data and querying has become a significant challenge; hence the graph database is emerging to address this challenge. Graph databases have the unique advantages of modelling and querying complex relationships, capturing and navigating complex data relationships and recursive path querying when handling graph data. In this thesis, we enhance graph databases from both system and algorithm perspectives. Firstly, we propose two systems, SQL2Cypher and FSPS, to improve the usability and efficiency of graph databases. SQL2Cypher automatically migrates data from a relational database to a graph database. This system also supports translating SQL queries into Cypher queries. FSPS is the first FPGA-based system for accelerating graph queries on massive graphs. FSPS has the following features 1) a CPU-FPGA co-designed framework, 2) a fully pipelined FPGA execution, and 3) reduced data transfer from FPGA’s external memory. FSPS supports the two most fundamental types of graph queries, namely subgraph and path queries. Performance evaluation shows that FSPS outperforms the most popular graph database, Neo4j, by up to three orders of magnitude. All the draft demo videos can be found at https://www.youtube.com/watch?v=oSpHtJ8iVio and https://www.youtube.com/watch?v=eGaeBrVTJws. Secondly, the graph database does not widely support the cohesive subgraph models (i.e., Neo4j and PatMat). Many real-world relationships can be naturally represented as bipartite graphs such as customer-product, user-item, and author-paper. Therefore, we use efficient construct algorithms to investigate the bipartite hierarchy model. The bipartite hierarchy is the first model to discover the hierarchical structure of bipartite graphs based on the concept of (alpha, beta)-core and graph connectivity. These algorithms can effectively identify the affected regions to limit computation scope and avoid re-building the bipartite hierarchy from scratch. Extensive experiments on 10 real-world graphs demonstrate the effectiveness of the proposed bipartite hierarchy and validate the efficiency of our hierarchy constructions algorithms

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

Efficient Community Search on Large Bipartite Graphs

In many real-world applications, bipartite graphs are naturally used to model relationships between two types of entities. Community discovery over bipartite graphs is a fundamental problem and has attracted much attention recently. However, all existing studies overlook the weight (e.g., influence or importance) of vertices in forming the community, thus missing useful properties of the community. In this thesis, we propose a novel cohesive subgraph model named Pareto-optimal (α, β)-community, which is the first to consider both structure cohesiveness and weight of vertices on bipartite graphs. The proposed Pareto-optimal (α, β)-community model follows the concept of (α, β)-core by im- posing degree constraints for each type of vertices, and integrates the Pareto-optimality in mod- eling the weight information from two different types of vertices. An online query algorithm is developed to retrieve Pareto-optimal (α, β)-communities with the time complexity of O(p · m) where p is the number of resulting communities, and m is the number of edges in the bipartite graph G. To support efficient query processing over large graphs, we also develop index-based approaches. A complete index is proposed, and the query algorithm based on I achieves linear query processing time regarding the result size (i.e., the algorithm is optimal). Nevertheless, the index incurs prohibitively expensive space complexity. To strike a balance between query effi- ciency and space complexity, a space-efficient compact index is proposed. Computation-sharing strategies are devised to improve the efficiency of the index construction process for the index. Extensive experiments on 9 real-world graphs validate both the effectiveness and the efficiency of our query processing algorithms and indexing techniques

Multi-Agent Pathfinding in Mixed Discrete-Continuous Time and Space

In the multi-agent pathfinding (MAPF) problem, agents must move from their current locations to their individual destinations while avoiding collisions. Ideally, agents move to their destinations as quickly and efficiently as possible. MAPF has many real-world applications such as navigation, warehouse automation, package delivery and games. Coordination of agents is necessary in order to avoid conflicts, however, it can be very computationally expensive to find mutually conflict-free paths for multiple agents – especially as the number of agents is increased. Existing state-ofthe- art algorithms have been focused on simplified problems on grids where agents have no shape or volume, and each action executed by the agents have the same duration, resulting in simplified collision detection and synchronous, timed execution. In the real world agents have a shape, and usually execute actions with variable duration. This thesis re-formulates the MAPF problem definition for continuous actions, designates specific techniques for continuous-time collision detection, re-formulates two popular algorithms for continuous actions and formulates a new algorithm called Conflict-Based Increasing Cost Search (CBICS) for continuous actions

Mining Butterflies in Streaming Graphs

This thesis introduces two main-memory systems sGrapp and sGradd for performing the fundamental analytic tasks of biclique counting and concept drift detection over a streaming graph. A data-driven heuristic is used to architect the systems. To this end, initially, the growth patterns of bipartite streaming graphs are mined and the emergence principles of streaming motifs are discovered. Next, the discovered principles are (a) explained by a graph generator called sGrow; and (b) utilized to establish the requirements for efficient, effective, explainable, and interpretable management and processing of streams. sGrow is used to benchmark stream analytics, particularly in the case of concept drift detection. sGrow displays robust realization of streaming growth patterns independent of initial conditions, scale and temporal characteristics, and model configurations. Extensive evaluations confirm the simultaneous effectiveness and efficiency of sGrapp and sGradd. sGrapp achieves mean absolute percentage error up to 0.05/0.14 for the cumulative butterfly count in streaming graphs with uniform/non-uniform temporal distribution and a processing throughput of 1.5 million data records per second. The throughput and estimation error of sGrapp are 160x higher and 0.02x lower than baselines. sGradd demonstrates an improving performance over time, achieves zero false detection rates when there is not any drift and when drift is already detected, and detects sequential drifts in zero to a few seconds after their occurrence regardless of drift intervals

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum