K-plex cover pooling for graph neural networks

Graph pooling methods provide mechanisms for structure reduction that are intended to ease the diffusion of context between nodes further in the graph, and that typically leverage community discovery mechanisms or node and edge pruning heuristics. In this paper, we introduce a novel pooling technique which borrows from classical results in graph theory that is non-parametric and generalizes well to graphs of different nature and connectivity patterns. Our pooling method, named KPlexPool, builds on the concepts of graph covers and k-plexes, i.e. pseudo-cliques where each node can miss up to k links. The experimental evaluation on benchmarks on molecular and social graph classification shows that KPlexPool achieves state of the art performances against both parametric and non-parametric pooling methods in the literature, despite generating pooled graphs based solely on topological information.

Finding Visible kNN Objects in the Presence of Obstacles within the User’s View Field †

In many spatial applications, users are only interested in data objects that are visible to them. Hence, finding visible data objects is an important operation in these real-world spatial applications. This study addressed a new type of spatial query, the View field-aware Visible k Nearest Neighbor (V2-kNN) query. Given the location of a user and his/her view field, a V2-kNN query finds data object p so that p is the nearest neighbor of and visible to the user, where visible means the data object is (1) not hidden by obstacles and (2) inside the view field of the user. Previous works on visible NN queries considered only one of these two factors, but not both. To the best of our knowledge, this work is the first to consider both the effect of obstacles and the restriction of the view field in finding the solutions. To support efficient processing of V2-kNN queries, a grid structure is used to index data objects and obstacles. Pruning heuristics are also designed so that only data objects and obstacles relevant to the final query result are accessed. A comprehensive experimental evaluation using both real and synthetic datasets is performed to verify the effectiveness of the proposed algorithms.

Effect-Abstraction Based Relaxation for Linear Numeric Planning

This paper studies an effect-abstraction based relaxation for reasoning about linear numeric planning problems. The effect-abstraction decomposes non-constant linear numeric effects into actions with conditional effects over additive constant numeric effects. With little effort, on this compiled version, it is possible to use known subgoaling based relaxations and relative heuristics. The combination of these two steps leads to a novel relaxation based heuristic. Theoretically, the relaxation is proved tighter than previous interval based relaxation and leading to safe-pruning heuristics. Empirically, a heuristic developed on this relaxation leads to substantial improvements for a class of problems that are currently out of the reach of state-of-the-art numeric planners.

A SPACE-EFFICIENT BACKTRACK-FREE REPRESENTATION FOR CONSTRAINT SATISFACTION PROBLEMS

In this paper we present a radical approach to obtaining a backtrack-free representation for a constraint satisfaction problem: remove values that lead to dead-ends. This technique does not require additional space but has the drawback of removing solutions. We investigate a number of variations on the basic algorithm including the use of seed solutions, consistency techniques, and a variety of pruning heuristics. Our experimental results indicate that a significant proportion of the solutions to the original problem can be retained especially when an optimization algorithm that specifically searches for such “good” backtrack-free representations is employed. Further extensions increase solution retention by searching for high-coverage backtrack-free representations, by removing tuples rather than values, and by combining multiple backtrack-free representations. Our approach elucidates, for the first time, a three-way trade-off between space complexity, potential backtracks, and solution loss and enables algorithms that can actively reason about the trade-off between space, backtracks, and solution loss.