In this paper, we address the problem of evaluating historical queries on graphs. To this end, we investigate the use of graph deltas, i.e., a log of time-annotated graph operations. Our storage model maintains the current graph snapshot and the delta. We reconstruct past snapshots by applying appropriate parts of the graph delta on the current snapshot. Query evaluation proceeds on the reconstructed snapshots but we also propose algorithms based mostly on deltas for efficiency. We introduce various techniques for improving performance, including materializing intermediate snapshots, partial reconstruction and indexing deltas.
The most relevant to our work is perhaps the historical graph structure recently proposed in @cite_14 . The authors consider a sequence of graphs produced as the graph evolves over time. Since the graphs in the sequence are very similar to each other, they propose computing graph representatives by clustering similar graphs and then storing appropriate differences from these representatives, instead of storing all graphs. Our approach is different in that we want to support a broad range of historical queries, not just queries that involve a single snapshot graph.
@cite_14
2154875162 1994840070 1992928799 2114216982
In many applications, information is best represented as graphs. In a dynamic world, information changes and so the graphs representing the information evolve with time. We propose that historical graph-structured data be maintained for analytical processing. We call a historical evolving graph sequence an EGS. We observe that in many applications, graphs of an EGS are large and numerous, and they often exhibit much redundancy among them. We study the problem of efficient query processing on an EGS and put forward a solution framework called FVF. Through extensive experiments on both real and synthetic datasets, we show that our FVF framework is highly efficient in EGS query processing. We consider the problem of representing graphs compactly while supporting queries efficiently. In particular we describe a data structure for representing n-vertex unlabeled graphs that satisfy an O(nc)-separator theorem, c < 1. The structure uses O(n) bits, and supports adjacency and degree queries in constant time, and neighbor listing in constant time per neighbor. This generalizes previous results for graphs with constant genus, such as planar graphs.We present experimental results using many "real world" graphs including 3-dimensional finite element meshes, link graphs of the web, internet router graphs, VLSI circuits, and street map graphs. Compared to adjacency lists, our approach reduces space usage by almost an order of magnitude, while supporting depthfirst traversal in about the same running time. Graph patterns are able to represent the complex structural relations among objects in many applications in various domains. The objective of graph summarization is to obtain a concise representation of a single large graph, which is interpretable and suitable for analysis. A good summary can reveal the hidden relationships between nodes in a graph. The key issue is how to construct a high-quality and representative super-graph, GS, in which a super-node summarizes a collection of nodes based on the similarity of attribute values and neighborhood relationships associated with nodes in G, and a super-edge summarizes the edges between nodes in G that are represented by two different super-nodes in GS. We propose an entropy-based unified model for measuring the homogeneity of the super-graph. The best summary in terms of homogeneity could be too large to explore. By using the unified model, we relax three summarization criteria to obtain an approximate homogeneous summary of reasonable size. We propose both ag- glomerative and divisive algorithms for approximate summarization, as well as pruning techniques and heuristics for both algorithms to save computation cost. Experimental results confirm that our approaches can efficiently generate high-quality summaries. We consider the problem of detecting past activities as well as anticipating which activity will happen in the future and how. We start by modeling the rich spatio-temporal relations between human poses and objects (called affordances) using a conditional random field (CRF). However, because of the ambiguity in the temporal segmentation of the sub-activities that constitute an activity, in the past as well as in the future, multiple graph structures are possible. In this paper, we reason about these alternate possibilities by reasoning over multiple possible graph structures. We obtain them by approximating the graph with only additive features, which lends to efficient dynamic programming. Starting with this proposal graph structure, we then design moves to obtain several other likely graph structures. We then show that our approach improves the state-of-the-art significantly for detecting past activities as well as for anticipating future activities, on a dataset of 120 activity videos collected from four subjects.