http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.

/pdf/approximate-nearest-neighbors-towards-removing-the-curse-of-27lmlz5prr.pdf

Approximate nearest neighbors: towards removing the curse of dimensionality

Fast and frugal heuristics - simple rules for making decisions with realistic mental resources - are presented here. These heuristics can enable both living organisms and artificial systems to make smart choices, classifications, and predictions by employing bounded rationality. But when and how can such fast and frugal heuristics work? What heuristics are in the mind's adaptive toolbox, and what building blocks compose them? Can judgments based simply on a single reason be as accurate as those based on many reasons? Could less knowledge even lead to systematically better predictions than more knowledge? This book explores these questions by developing computational models of heuristics and testing them through experiments and analysis. It shows how fast and frugal heuristics can yield adaptive decisions in situations as varied as choosing a mate, dividing resources among offspring, predicting high school drop-out rates, and playing the stock market.

Simple Heuristics That Make Us Smart

Mobile ad hoc routing protocols allow nodes with wireless adaptors to communicate with one another without any pre-existing network infrastructure. Existing ad hoc routing protocols, while robust to rapidly changing network topology, assume the presence of a connected path from source to destination. Given power limitations, the advent of short-range wireless networks, and the wide physical conditions over which ad hoc networks must be deployed, in some scenarios it is likely that this assumption is invalid. In this work, we develop techniques to deliver messages in the case where there is never a connected path from source to destination or when a network partition exists at the time a message is originated. To this end, we introduce Epidemic Routing, where random pair-wise exchanges of messages among mobile hosts ensure eventual message delivery. The goals of Epidemic Routing are to: i) maximize message delivery rate, ii) minimize message latency, and iii) minimize the total resources consumed in message delivery. Through an implementation in the Monarch simulator, we show that Epidemic Routing achieves eventual delivery of 100% of messages with reasonable aggregate resource consumption in a number of interesting scenarios.

/pdf/epidemic-routing-for-partially-connected-ad-hoc-networks-s5rslcaiip.pdf

Epidemic routing for partially-connected ad hoc networks

Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Analytic Combinatorics

Whru a dilt~lhSC is replicated at, many sites2 maintaining mutual consistrnry among t,he sites iu the fac:e of updat,es is a signitirant problem. This paper descrikrs several randomized algorit,hms for dist,rihut.ing updates and driving t,he replicas toward consist,c>nc,y. The algorit Inns are very simple and require few guarant,ees from the underlying conllllunicat.ioll system, yc+ they rnsutc t.hat. the off(~c~t, of (‘very update is evcnt,uwlly rf+irt-ted in a11 rq1ica.s. The cost, and parformancc of t,hr algorithms arc tuned I>? c%oosing appropriat,c dist,rilMions in t,hc randoinizat,ioii step. TIN> idgoritlmls ilr(’ c*los~*ly analogoIls t,o epidemics, and t,he epidcWliolog)litc\ratiirc, ilitlh iii Illld~~rsti4lldill~ tlicir bc*liavior. One of tlW i$,oritlims 11&S brc>n implrmcWrd in the Clraringhousr sprv(brs of thr Xerox C’orporat~c~ Iiitcrnc4, solviiig long-standing prol>lf~lns of high traffic and tlatirl>ilsr inconsistcllcp.

http://bitsavers.informatik.uni-stuttgart.de/pdf/xerox/parc/techReports/CSL-89-1_Epidemic_Algorithms_for_Replicated_Database_Maintenance.pdf

Epidemic algorithms for replicated database maintenance

When a database is replicated at many sites, maintaining mutual consistency among the sites in the face of updates is a significant problem. This paper describes several randomized algorithms for distributing updates and driving the replicas toward consistency. The algorithms are very simple and require few guarantees from the underlying communication system, yet they ensure that the effect of every update is eventually reflected in all replicas. The cost and performance of the algorithms are tuned by choosing appropriate distributions in the randomization step. The algorithms are closely analogous to epidemics, and the epidemiology literature aids in understanding their behavior. One of the algorithms has been implemented in the Clearinghouse servers of the Xerox Corporate Internet. solving long-standing problems of high traffic and database inconsistency.

In order to meet performance goals, it is widely agreed that vehicular ad hoc networks (VANETs) must rely heavily on node-to-node communication, thus allowing for malicious data traffic. At the same time, the easy access to information afforded by VANETs potentially enables the difficult security goal of data validation. We propose a general approach to evaluating the validity of VANET data. In our approach a node searches for possible explanations for the data it has collected based on the fact that malicious nodes may be present. Explanations that are consistent with the node's model of the VANET are scored and the node accepts the data as dictated by the highest scoring explanations. Our techniques for generating and scoring explanations rely on two assumptions: 1) nodes can tell "at least some" other nodes apart from one another and 2) a parsimony argument accurately reflects adversarial behavior in a VANET. We justify both assumptions and demonstrate our approach on specific VANETs.

/pdf/detecting-and-correcting-malicious-data-in-vanets-15bb5xtbn1.pdf

Detecting and correcting malicious data in VANETs

In a clustering problem, the aim is to partition a given set of n points in d-dimensional space into k groups, called clusters, so that points within each cluster are near each other. Two objective functions frequently used to measure the performance of a clustering algorithm are, for any L4 metric, (a) the maximum distance between pairs of points in the same cluster, and (b) the maximum distance between points in each cluster and a chosen cluster center; we refer to either measure as the cluster size.We show that one cannot approximate the optimal cluster size for a fixed number of clusters within a factor close to 2 in polynomial time, for two or more dimensions, unless P=NP. We also present an algorithm that achieves this factor of 2 in time O(n log k), and show that this running time is optimal in the algebraic decision tree model. For a fixed cluster size, on the other hand, we give a polynomial time approximation scheme that estimates the optimal number of clusters under the second measure of cluster size within factors arbitrarily close to 1. Our approach is extended to provide approximation algorithms for the restricted centers, suppliers, and weighted suppliers problems that run in optimal O(n log k) time and achieve optimal or nearly optimal approximation bounds.

Optimal algorithms for approximate clustering

Preface Binomial Identities.- Summary of Useful Identities.- Deriving the Identities.- Inverse Relations.- Operator Calculus.- Hypergeometric Series.- Identities with the Harmonic Numbers Recurrence Relations.- Linear Recurrence Relations.- Nonlinear Recurrence Relations Operator Methods.- The Cookie Monster.- Coalesced Hashing.- Open Addressing: Uniform Hashing.- Open Addressing: Secondary Clustering Asymptotic Analysis.- Basic Concepts.- Stieltjes Integration and Asymptotics.- Asymptotics from Generating Functions Bibliography Appendices.- Schedule of Lectures.- Homework Assignments.- Midterm Exam I and Solutions.- Final Exam I and Solutions.- Midterm Exam II and Solutions.- Final Exam II and Solutions.- Midterm Exam III and Solutions.- Final Exam III and Solutions.- A Qualifying Exam Problem and Solution Index

Daniel H. Greene

Papers

Epidemic algorithms for replicated database maintenance

Epidemic algorithms for replicated database maintenance

Detecting and correcting malicious data in VANETs

Optimal algorithms for approximate clustering

Mathematics for the Analysis of Algorithms