Temporal Graph Traversals: Definitions, Algorithms, and Applications

A temporal graph is a graph in which connections between vertices are active at specific times, and such temporal information leads to completely new patterns and knowledge that are not present in a non-temporal graph. In this paper, we study traversal problems in a temporal graph. Graph traversals, such as DFS and BFS, are basic operations for processing and studying a graph. While both DFS and BFS are well-known simple concepts, it is non-trivial to adopt the same notions from a non-temporal graph to a temporal graph. We analyze the difficulties of defining temporal graph traversals and propose new definitions of DFS and BFS for a temporal graph. We investigate the properties of temporal DFS and BFS, and propose efficient algorithms with optimal complexity. In particular, we also study important applications of temporal DFS and BFS. We verify the efficiency and importance of our graph traversal algorithms in real world temporal graphs

Efficient mining of discriminative molecular fragments

Frequent pattern discovery in structured data is receiving an increasing attention in many application areas of sciences. However, the computational complexity and the large amount of data to be explored often make the sequential algorithms unsuitable. In this context high performance distributed computing becomes a very interesting and promising approach. In this paper we present a parallel formulation of the frequent subgraph mining problem to discover interesting patterns in molecular compounds. The application is characterized by a highly irregular tree-structured computation. No estimation is available for task workloads, which show a power-law distribution in a wide range. The proposed approach allows dynamic resource aggregation and provides fault and latency tolerance. These features make the distributed application suitable for multi-domain heterogeneous environments, such as computational Grids. The distributed application has been evaluated on the well known National Cancer Institute’s HIV-screening dataset

A Proof Strategy Language and Proof Script Generation for Isabelle/HOL

We introduce a language, PSL, designed to capture high level proof strategies in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system generates and combines various tactics to explore a large search space with low memory usage. Upon success, PSL generates an efficient proof script, which bypasses a large part of the proof search. We also present PSL's monadic interpreter to show that the underlying idea of PSL is transferable to other ITPs.Comment: This paper has been submitted to CADE2

High performance subgraph mining in molecular compounds

Structured data represented in the form of graphs arises in several fields of the science and the growing amount of available data makes distributed graph mining techniques particularly relevant. In this paper, we present a distributed approach to the frequent subgraph mining problem to discover interesting patterns in molecular compounds. The problem is characterized by a highly irregular search tree, whereby no reliable workload prediction is available. We describe the three main aspects of the proposed distributed algorithm, namely a dynamic partitioning of the search space, a distribution process based on a peer-to-peer communication framework, and a novel receiver-initiated, load balancing algorithm. The effectiveness of the distributed method has been evaluated on the well-known National Cancer Institute’s HIV-screening dataset, where the approach attains close-to linear speedup in a network of workstations

Generalizing backdoors

Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.

PReaCH: A Fast Lightweight Reachability Index using Pruning and Contraction Hierarchies

We develop the data structure PReaCH (for Pruned Reachability Contraction Hierarchies) which supports reachability queries in a directed graph, i.e., it supports queries that ask whether two nodes in the graph are connected by a directed path. PReaCH adapts the contraction hierarchy speedup techniques for shortest path queries to the reachability setting. The resulting approach is surprisingly simple and guarantees linear space and near linear preprocessing time. Orthogonally to that, we improve existing pruning techniques for the search by gathering more information from a single DFS-traversal of the graph. PReaCH-indices significantly outperform previous data structures with comparable preprocessing cost. Methods with faster queries need significantly more preprocessing time in particular for the most difficult instances