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

Most statistical and machine-learning algorithms assume that the data is a random sample drawn from a stationary distribution. Unfortunately, most of the large databases available for mining today violate this assumption. They were gathered over months or years, and the underlying processes generating them changed during this time, sometimes radically. Although a number of algorithms have been proposed for learning time-changing concepts, they generally do not scale well to very large databases. In this paper we propose an efficient algorithm for mining decision trees from continuously-changing data streams, based on the ultra-fast VFDT decision tree learner. This algorithm, called CVFDT, stays current while making the most of old data by growing an alternative subtree whenever an old one becomes questionable, and replacing the old with the new when the new becomes more accurate. CVFDT learns a model which is similar in accuracy to the one that would be learned by reapplying VFDT to a moving window of examples every time a new example arrives, but with O(1) complexity per example, as opposed to O(w), where w is the size of the window. Experiments on a set of large time-changing data streams demonstrate the utility of this approach.

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Mining time-changing data streams

The dynamic and lossy nature of wireless communication poses major challenges to reliable, self-organizing multihop networks. These non-ideal characteristics are more problematic with the primitive, low-power radio transceivers found in sensor networks, and raise new issues that routing protocols must address. Link connectivity statistics should be captured dynamically through an efficient yet adaptive link estimator and routing decisions should exploit such connectivity statistics to achieve reliability. Link status and routing information must be maintained in a neighborhood table with constant space regardless of cell density. We study and evaluate link estimator, neighborhood table management, and reliable routing protocol techniques. We focus on a many-to-one, periodic data collection workload. We narrow the design space through evaluations on large-scale, high-level simulations to 50-node, in-depth empirical experiments. The most effective solution uses a simple time averaged EWMA estimator, frequency based table management, and cost-based routing.

/pdf/taming-the-underlying-challenges-of-reliable-multihop-2e2c4yefix.pdf

Taming the underlying challenges of reliable multihop routing in sensor networks

In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has emerged for reasoning about algorithms that work within these constraints on space, time, and number of passes. Some of the methods rely on metric embeddings, pseudo-random computations, sparse approximation theory and communication complexity. The applications for this scenario include IP network traffic analysis, mining text message streams and processing massive data sets in general. Researchers in Theoretical Computer Science, Databases, IP Networking and Computer Systems are working on the data stream challenges. This article is an overview and survey of data stream algorithmics and is an updated version of [1].

/pdf/data-streams-algorithms-and-applications-5fo85u5tcy.pdf

Data streams: algorithms and applications

Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics.

The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area.

The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.

The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming.

- Covers the whole field of constraint programming
- Survey-style chapters
- Five chapters on applications

Table of Contents

Foreword (Ugo Montanari) 
Part I : Foundations
Chapter 1. Introduction (Francesca Rossi, Peter van Beek, Toby Walsh) 
Chapter 2. Constraint Satisfaction: An Emerging Paradigm (Eugene C. Freuder, Alan K. Mackworth) 
Chapter 3. Constraint Propagation (Christian Bessiere) 
Chapter 4. Backtracking Search Algorithms (Peter van Beek) 
Chapter 5. Local Search Methods (Holger H. Hoos, Edward Tsang) 
Chapter 6. Global Constraints (Willem-Jan van Hoeve, Irit Katriel)
Chapter 7. Tractable Structures for CSPs (Rina Dechter)
Chapter 8. The Complexity of Constraint Languages
(David Cohen, Peter Jeavons) 
Chapter 9. Soft Constraints (Pedro Meseguer, Francesca Rossi, Thomas Schiex) 
Chapter 10. Symmetry in Constraint Programming
(Ian P. Gent, Karen E. Petrie, Jean-Francois Puget)
Chapter 11. Modelling (Barbara M. Smith) 
Part II : Extensions, Languages, and Applications

Chapter 12. Constraint Logic Programming (Kim Marriott, Peter J. Stuckey, Mark Wallace) 
Chapter 13. Constraints in Procedural and Concurrent Languages (Thom Fruehwirth, Laurent Michel, Christian Schulte)
Chapter 14. Finite Domain Constraint Programming Systems (Christian Schulte, Mats Carlsson) 
Chapter 15. Operations Research Methods in Constraint Programming (John Hooker) 
Chapter 16. Continuous and Interval Constraints(Frederic Benhamou, Laurent Granvilliers) 
Chapter 17. Constraints over Structured Domains
(Carmen Gervet) 
Chapter 18. Randomness and Structure (Carla Gomes, Toby Walsh)
Chapter 19. Temporal CSPs (Manolis Koubarakis)
Chapter 20. Distributed Constraint Programming
(Boi Faltings) 
Chapter 21. Uncertainty and Change (Kenneth N. Brown, Ian Miguel)
Chapter 22. Constraint-Based Scheduling and Planning
(Philippe Baptiste, Philippe Laborie, Claude Le Pape, Wim Nuijten)
Chapter 23. Vehicle Routing (Philip Kilby, Paul Shaw) 
Chapter 24. Configuration (Ulrich Junker)
Chapter 25. Constraint Applications in Networks
(Helmut Simonis)
Chapter 26. Bioinformatics and Constraints (Rolf Backofen, David Gilbert)

/pdf/handbook-of-constraint-programming-53srutguo2.pdf

Handbook of Constraint Programming

We study the problem of on-line searching for a target inside a polygon. In particular, we propose a strategy for finding a target of unknown location in a star-shaped polygon with a competitive ratio of 11.52. We also provide a lower bound of 9 for the competitive ratio of searching in a star-shaped polygon which is close to the upper bound. A similar task is the on-line recognition of a star-shaped polygon P. Here, the robot travels on a path that allows it to decide whether P is star-shaped or not. We present a strategy with a competitive ratio of 28.85 and give a lower bound of √82 for this problem.

Searching and on-line recognition of star-shaped polygons

We introduce the k-H-Packing with t-Overlap problem to formalize the problem of discovering overlapping communities in real networks. More precisely, in the k-H-Packing with t-Overlap problem, we search in a graph G for at least k subgraphs each isomorphic to a graph H such that any pair of subgraphs shares at most t vertices. In contrast with previous work where communities are disjoint, we regulate the overlap through a variable t. Our focus is on the parameterized complexity of the k-H-Packing with t-Overlap problem. Here, we provide a new technique for this problem generalizing the crown decomposition technique [2]. Using our global rule, we achieve a kernel with size bounded by 2(rk r) for the k-Kr-Packing with (r 2)Overlap problem. That is, when H is a clique of size r and t = r 2. In addition, we introduce the first parameterized algorithm for the kH-Packing with t-Overlap problem when H is an arbitrary graph of size r. Our algorithm combines a bounded search tree with a greedy localization technique and runs in time O(r rk k (r t 1)k+2 n r ), where n = |V (G)|, r = |V (H)|, and t < r. Finally, we apply this search tree algorithm to the kernel obtained for the k-Kr-Packing with (r 2)-Overlap problem, and we show that this approach is faster than applying a brute-force algorithm in the kernel. In all our results, r and t are constants.

Parameterized Algorithms for the H-Packing with t-Overlap Problem

Valiant load balancing (VLB), also called two-stage load balancing, is gaining popularity as a routing scheme that can serve arbitrary traffic matrices. To date, VLB network design is well understood on a logical full-mesh topology, where VLB is optimal even when nodes can fail. In this paper, we address the design and capacity provisioning of arbitrary VLB network topologies. First, we introduce an algorithm to determine if VLB can serve all traffic matrices when a fixed number of arbitrary links fail, and we show how to find a min-cost expansion of the network - via link upgrades and installs - so that it is resilient to these failures. Additionally, we propose a method to design a new VLB network under the fixed-charge network design cost model. Finally, we prove that VLB is no longer optimal on unrestricted topologies, and can require more capacity than shortest path routing to serve all traffic matrices on some topologies. These results rely on a novel theorem that characterizes the capacity VLB requires of links crossing each cut, i.e., a partition, of the network's nodes.

/pdf/capacity-provisioning-a-valiant-load-balanced-network-4dwy6aqw9h.pdf

Capacity Provisioning a Valiant Load-Balanced Network

We consider two variants of the well-known "sailor in the fog" puzzle. The first version (the "asteroid surveying" problem) is set in three dimensions and asks for the shortest curve that starts at the origin and intersects all planes at unit distance from the origin. Several possible solutions are suggested in the video, including a curve of length less than 12.08. The second version (the "river shore" problem) asks for the shortest curve in the plane that has unit width. A solution of length 2.2782 is described, which we have proved to be optimal.

The asteroid surveying problem and other puzzles

We present and analyze methods for patrolling and surveillance in an environment with a distributed swarm of robots with limited capabilities. Our approach is based on a distributed triangulation of the work space, in which a set of p stationary sensors provides coverage control; in addition, there are r mobile robots that can move between the sensors. Building on our prior work on structured exploration of unknown spaces with multi-robot systems, we can make use of a triangulation that is constructed in a distributed fashion and guarantees good local navigation properties, even when sensors and robots have very limited capabilities.

Alejandro López-Ortiz

Papers

Searching and on-line recognition of star-shaped polygons

Parameterized Algorithms for the H-Packing with t-Overlap Problem

Capacity Provisioning a Valiant Load-Balanced Network

The asteroid surveying problem and other puzzles

Local policies for efficiently patrolling a triangulated region by a robot swarm