We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.

Probability and Random Processes

The relative ineffectiveness of information retrieval systems is largely caused by the inaccuracy with which a query formed by a few keywords models the actual user information need. One well known method to overcome this limitation is automatic query expansion (AQE), whereby the user’s original query is augmented by new features with a similar meaning. AQE has a long history in the information retrieval community but it is only in the last years that it has reached a level of scientific and experimental maturity, especially in laboratory settings such as TREC. This survey presents a unified view of a large number of recent approaches to AQE that leverage various data sources and employ very different principles and techniques. The following questions are addressed. Why is query expansion so important to improve search effectiveness? What are the main steps involved in the design and implementation of an AQE component? What approaches to AQE are available and how do they compare? Which issues must still be resolved before AQE becomes a standard component of large operational information retrieval systems (e.g., search engines)?

/pdf/a-survey-of-automatic-query-expansion-in-information-30cfvdlacg.pdf

A Survey of Automatic Query Expansion in Information Retrieval

https://pure.mpg.de/pubman/item/item_1819068_3/component/file_1840695/MPI-I-2007-5-003.pdf

YAGO: A Large Ontology from Wikipedia and WordNet

We present a route planning technique solely based on the concept of node contraction. The nodes are first ordered by 'importance'. A hierarchy is then generated by iteratively contracting the least important node. Contracting a node υ means replacing shortest paths going through v by shortcuts. We obtain a hierarchical query algorithm using bidirectional shortest-path search. The forward search uses only edges leading to more important nodes and the backward search uses only edges coming from more important nodes. For fastest routes in road networks, the graph remains very sparse throughout the contraction process using rather simple heuristics for ordering the nodes. We have five times lower query times than the best previous hierarchical Dijkstra-based speedup techniques and a negative space overhead, i.e., the data structure for distance computation needs less space than the input graph. CHs can be combined with many other route planning techniques, leading to improved performance for many-to-many routing, transit-node routing, goal-directed routing or mobile and dynamic scenarios.

/pdf/contraction-hierarchies-faster-and-simpler-hierarchical-44o5lbyhfa.pdf

Contraction hierarchies: faster and simpler hierarchical routing in road networks

When you drive to somewhere far away, you will leave your current location via one of only a few important traffic junctions. Starting from this informal observation, we developed an algorithmic approach, transit node routing, that allows us to reduce quickest path queries in road networks to a small number of table lookups. For road maps of Western Europe and the United States, our best query times improved over the best previously published figures by two orders of magnitude. This is also more than one million times faster than the best known algorithm for general networks.

https://science.sciencemag.org/content/sci/316/5824/566.full.pdf

Fast Routing in Road Networks with Transit Nodes

We consider the following full-text search autocompletion feature. Imagine a user of a search engine typing a query. Then with every letter being typed, we would like an instant display of completions of the last query word which would lead to good hits. At the same time, the best hits for any of these completions should be displayed. Known indexing data structures that apply to this problem either incur large processing times for a substantial class of queries, or they use a lot of space. We present a new indexing data structure that uses no more space than a state-of-the-art compressed inverted index, but with 10 times faster query processing times. Even on the large TREC Terabyte collection, which comprises over 25 million documents, we achieve, on a single machine and with the index on disk, average response times of one tenth of a second. We have built a full-fledged, interactive search engine that realizes the proposed autocompletion feature combined with support for proximity search, semi-structured (XML) text, subword and phrase completion, and semantic tags.

Type less, find more: fast autocompletion search with a succinct index

When you drive to somewhere 'far away', you will leave your current location via one of only a few 'important' traffic junctions. Starting from this informal observation, we develop an algorithmic approach---transit node routing---that allows us to reduce quickest-path queries in road networks to a small number of table lookups. We present two implementations of this idea, one based on a simple grid data structure and one based on highway hierarchies. For the road map of the United States, our best query times improve over the best previously published figures by two orders of magnitude. Our results exhibit various trade-offs between average query time (5 μs to 63 μs), preprocessing time (59 min to 1200 min), and storage overhead (21 bytes/node to 244 bytes/node).

/pdf/in-transit-to-constant-time-shortest-path-queries-in-road-4zhjvyccak.pdf

Holger Bast

Papers

Fast Routing in Road Networks with Transit Nodes

Type less, find more: fast autocompletion search with a succinct index

In transit to constant time shortest-path queries in road networks

In transit to constant time shortest-path queries in road networks

IO-Top-k: Index-Access Optimized Top-k Query Processing