On Learning Counting Functions With Queries

We investigate the problem of learning disjunctions of counting functions, which are general cases of parity and modulo functions, with equivalence and membership queries. We prove that, for any prime number p, the class of disjunctions of integer-weighted counting functions with modulus p over the domain Znq (or Zn) for any given integer q ≥ 2 is polynomial time learnable using at most n + 1 equivalence queries, where the hypotheses issued by the learner are disjunctions of at most n counting functions with weights from Zp. The result is obtained through learning linear systems over an arbitrary field. In general a counting function may have a composite modulus. We prove that, for any given integer q ≥ 2, over the domain Zn2, the class of read-once disjunctions of Boolean-weighted counting functions with modulus q is polynomial time learnable with only one equivalence query, and the class of disjunctions of log log n Boolean-weighted counting functions with modulus q is polynomial time learnable. Finally, we present an algorithm for learning graph-based counting functions.

On the Emergence of Highly Variable Distributions in the Autonomous System Topology

Recent studies have noted that vertex degree in the autonomous system (AS) graph exhibits a highly variable distribution [15, 22]. The most prominent explanatory model for this phenomenon is the Barabási-Albert (B-A) model [5, 2]. A central feature of the B-A model is preferential connectivity—meaning that the likelihood a new node in a growing graph will connect to an existing node is proportional to the existing node’s degree. In this paper we ask whether a more general explanation than the B-A model, and absent the assumption of preferential connectivity, is consistent with empirical data. We are motivated by two observations: first, AS degree and AS size are highly correlated [11]; and second, highly variable AS size can arise simply through exponential growth. We construct a model incorporating exponential growth in the size of the Internet, and in the number of ASes. We then show via analysis that such a model yields a size distribution exhibiting a power-law tail. In such a model, if an AS’s link formation is roughly proportional to its size, then AS degree will also show high variability. We instantiate such a model with empirically derived estimates of growth rates and show that the resulting degree distribution is in good agreement with that of real AS graphs.

BRITE: Universal Topology Generation from a User's Perspective

Effective engineering of the Internet is predicated upon a detailed understanding of issues such as the large-scale structure of its underlying physical topology, the manner in which it evolves over time, and the way in which its constituent components contribute to its overall function. Unfortunately, developing a deep understanding of these issues has proven to be a challenging task, since it in turn involves solving difficult problems such as mapping the actual topology, characterizing it, and developing models that capture its emergent behavior. Consequently, even though there are a number of topology models, it is an open question as to how representative the topologies they generate are of the actual Internet. Our goal is to produce a topology generation framework which improves the state of the art and is based on design principles which include representativeness, inclusiveness, and interoperability. Representativeness leads to synthetic topologies that accurately reflect many aspects of the actual Internet topology (e.g. hierarchical structure, degree distribution, etc.). Inclusiveness combines the strengths of as many generation models as possible in a single generation tool. Interoperability provides interfaces to widely-used simulation and visualization applications such as ns and SSF. We call such a tool a universal topology generator. In this paper we discuss the design, implementation and usage of the BRITE universal topology generation tool that we have built. We also describe the BRITE Analysis Engine, BRIANA, which is an independent piece of software designed and built upon BRITE design goals of flexibility and extensibility. The purpose of BRIANA is to act as a repository of analysis routines along with a user–friendly interface that allows its use on different topology formats.

Sampling Biases in IP Topology Measurements

Considerable attention has been focused on the properties of graphs derived from Internet measurements. Router-level topologies collected via traceroute studies have led some authors to conclude that the router graph of the Internet is a scale-free graph, or more generally a power-law random graph. In such a graph, the degree distribution of nodes follows a distribution with a power-law tail. In this paper we argue that the evidence to date for this conclusion is at best insufficient. We show that graphs appearing to have power-law degree distributions can arise surprisingly easily, when sampling graphs whose true degree distribution is not at all like a power-law. For example, given a classical Erdös-Rényi sparse, random graph, the subgraph formed by a collection of shortest paths from a small set of random sources to a larger set of random destinations can easily appear to show a degree distribution remarkably like a power-law. We explore the reasons for how this effect arises, and show that in such a setting, edges are sampled in a highly biased manner. This insight allows us to distinguish measurements taken from the Erdös-Rényi graphs from those taken from power-law random graphs. When we apply this distinction to a number of well-known datasets, we find that the evidence for sampling bias in these datasets is strong.

On the Intrinsic Locality Properties of Web Reference Streams

There has been considerable work done in the study of Web reference streams: sequences of requests for Web objects. In particular, many studies have looked at the locality properties of such streams, because of the impact of locality on the design and performance of caching and prefetching systems. However, a general framework for understanding why reference streams exhibit given locality properties has not yet emerged. In this work we take a first step in this direction, based on viewing the Web as a set of reference streams that are transformed by Web components (clients, servers, and intermediaries). We propose a graph-based framework for describing this collection of streams and components. We identify three basic stream transformations that occur at nodes of the graph: aggregation, disaggregation and filtering, and we show how these transformations can be used to abstract the effects of different Web components on their associated reference streams. This view allows a structured approach to the analysis of why reference streams show given properties at different points in the Web. Applying this approach to the study of locality requires good metrics for locality. These metrics must meet three criteria: 1) they must accurately capture temporal locality; 2) they must be independent of trace artifacts such as trace length; and 3) they must not involve manual procedures or model-based assumptions. We describe two metrics meeting these criteria that each capture a different kind of temporal locality in reference streams. The popularity component of temporal locality is captured by entropy, while the correlation component is captured by interreference coefficient of variation. We argue that these metrics are more natural and more useful than previously proposed metrics for temporal locality. We use this framework to analyze a diverse set of Web reference traces. We find that this framework can shed light on how and why locality properties vary across different locations in the Web topology. For example, we find that filtering and aggregation have opposing effects on the popularity component of the temporal locality, which helps to explain why multilevel caching can be effective in the Web. Furthermore, we find that all transformations tend to diminish the correlation component of temporal locality, which has implications for the utility of different cache replacement policies at different points in the Web.

On the Stable Paths Problem and a Restricted Variant

Interdomain routing on the Internet is performed using route preference policies specified independently, and arbitrarily by each Autonomous System in the network. These policies are used in the border gateway protocol (BGP) by each AS when selecting next-hop choices for routes to each destination. Conflicts between policies used by different ASs can lead to routing instabilities that, potentially, cannot be resolved no matter how long BGP is run. The Stable Paths Problem (SPP) is an abstract graph theoretic model of the problem of selecting nexthop routes for a destination. A stable solution to the problem is a set of next-hop choices, one for each AS, that is compatible with the policies of each AS. In a stable solution each AS has selected its best next-hop given that the next-hop choices of all neighbors are fixed. BGP can be viewed as a distributed algorithm for solving SPP. In this report we consider the stable paths problem, as well as a family of restricted variants of the stable paths problem, which we call F stable paths problems. We show that two very simple variants of the stable paths problem are also NP-complete. In addition we show that for networks with a DAG topology, there is an efficient centralized algorithm to solve the stable paths problem, and that BGP always efficiently converges to a stable solution on such networks.

Indexing Distances in Large Graphs and Applications in Search Tasks

This thesis elaborates on the problem of preprocessing a large graph so that single-pair shortest-path queries can be answered quickly at runtime. Computing shortest paths is a well studied problem, but exact algorithms do not scale well to real-world huge graphs in applications that require very short response time. The focus is on approximate methods for distance estimation, in particular in landmarks-based distance indexing. This approach involves choosing some nodes as landmarks and computing (offline), for each node in the graph its embedding, i.e., the vector of its distances from all the landmarks. At runtime, when the distance between a pair of nodes is queried, it can be quickly estimated by combining the embeddings of the two nodes. Choosing optimal landmarks is shown to be hard and thus heuristic solutions are employed. Given a budget of memory for the index, which translates directly into a budget of landmarks, different landmark selection strategies can yield dramatically different results in terms of accuracy. A number of simple methods that scale well to large graphs are therefore developed and experimentally compared. The simplest methods choose central nodes of the graph, while the more elaborate ones select central nodes that are also far away from one another. The efficiency of the techniques presented in this thesis is tested experimentally using five different real world graphs with millions of edges; for a given accuracy, they require as much as 250 times less space than the current approach which considers selecting landmarks at random. Finally, they are applied in two important problems arising naturally in large-scale graphs, namely social search and community detection.

Foundational Theory for Understanding Policy Routing Dynamics

In this paper we introduce a theory of policy routing dynamics based on fundamental axioms of routing update mechanisms. We develop a dynamic policy routing model (DPR) that extends the static formalism of the stable paths problem (introduced by Griffin et al.) with discrete synchronous time. DPR captures the propagation of path changes in any dynamic network irrespective of its time-varying topology. We introduce several novel structures such as causation chains, dispute fences and policy digraphs that model different aspects of routing dynamics and provide insight into how these dynamics manifest in a network. We exercise the practicality of the theoretical foundation provided by DPR with two fundamental problems: routing dynamics minimization and policy conflict detection. The dynamics minimization problem utilizes policy digraphs, that capture the dependencies in routing policies irrespective of underlying topology dynamics, to solve a graph optimization problem. This optimization problem explicitly minimizes the number of routing update messages in a dynamic network by optimally changing the path preferences of a minimal subset of nodes. The conflict detection problem, on the other hand, utilizes a theoretical result of DPR where the root cause of a causation cycle (i.e., cycle of routing update messages) can be precisely inferred as either a transient route flap or a dispute wheel (i.e., policy conflict). Using this result we develop SafetyPulse, a token-based distributed algorithm to detect policy conflicts in a dynamic network. SafetyPulse is privacy preserving, computationally efficient, and provably correct.

Fast Shortest Path Distance Estimation in Large Networks

We study the problem of preprocessing a large graph so that point-to-point shortest-path queries can be answered very fast. Computing shortest paths is a well studied problem, but exact algorithms do not scale to huge graphs encountered on the web, social networks, and other applications. In this paper we focus on approximate methods for distance estimation, in particular using landmark-based distance indexing. This approach involves selecting a subset of nodes as landmarks and computing (offline) the distances from each node in the graph to those landmarks. At runtime, when the distance between a pair of nodes is needed, we can estimate it quickly by combining the precomputed distances of the two nodes to the landmarks. We prove that selecting the optimal set of landmarks is an NP-hard problem, and thus heuristic solutions need to be employed. Given a budget of memory for the index, which translates directly into a budget of landmarks, different landmark selection strategies can yield dramatically different results in terms of accuracy. A number of simple methods that scale well to large graphs are therefore developed and experimentally compared. The simplest methods choose central nodes of the graph, while the more elaborate ones select central nodes that are also far away from one another. The efficiency of the suggested techniques is tested experimentally using five different real world graphs with millions of edges; for a given accuracy, they require as much as 250 times less space than the current approach in the literature which considers selecting landmarks at random. Finally, we study applications of our method in two problems arising naturally in large-scale networks, namely, social search and community detection.

Nearest-neighbor Queries in Probabilistic Graphs

Large probabilistic graphs arise in various domains spanning from social networks to biological and communication networks. An important query in these graphs is the k nearest-neighbor query, which involves finding and reporting the k closest nodes to a specific node. This query assumes the existence of a measure of the "proximity" or the "distance" between any two nodes in the graph. To that end, we propose various novel distance functions that extend well known notions of classical graph theory, such as shortest paths and random walks. We argue that many meaningful distance functions are computationally intractable to compute exactly. Thus, in order to process nearest-neighbor queries, we resort to Monte Carlo sampling and exploit novel graph-transformation ideas and pruning opportunities. In our extensive experimental analysis, we explore the trade-offs of our approximation algorithms and demonstrate that they scale well on real-world probabilistic graphs with tens of millions of edges.

Comparison of K-ary N-cube and de Bruijn Overlays in QoS-Constrained Multicast Applications

Research on the construction of logical overlay networks has gained significance in recent times. This is partly due to work on peer-to-peer (P2P) systems for locating and retrieving distributed data objects, and also scalable content distribution using end-system multicast techniques. However, there are emerging applications that require the real-time transport of data from various sources to potentially many thousands of subscribers, each having their own quality-of-service (QoS) constraints. This paper primarily focuses on the properties of two popular topologies found in interconnection networks, namely k-ary n-cubes and de Bruijn graphs. The regular structure of these graph topologies makes them easier to analyze and determine possible routes for real-time data than complete or irregular graphs. We show how these overlay topologies compare in their ability to deliver data according to the QoS constraints of many subscribers, each receiving data from specific publishing hosts. Comparisons are drawn on the ability of each topology to route data in the presence of dynamic system effects, due to end-hosts joining and departing the system. Finally, experimental results show the service guarantees and physical link stress resulting from efficient multicast trees constructed over both kinds of overlay networks.

Face Identification by a Cascade of Rejection Classifiers

Nearest neighbor search is commonly employed in face recognition but it does not scale well to large dataset sizes. A strategy to combine rejection classifiers into a cascade for face identification is proposed in this paper. A rejection classifier for a pair of classes is defined to reject at least one of the classes with high confidence. These rejection classifiers are able to share discriminants in feature space and at the same time have high confidence in the rejection decision. In the face identification problem, it is possible that a pair of known individual faces are very dissimilar. It is very unlikely that both of them are close to an unknown face in the feature space. Hence, only one of them needs to be considered. Using a cascade structure of rejection classifiers, the scope of nearest neighbor search can be reduced significantly. Experiments on Face Recognition Grand Challenge (FRGC) version 1 data demonstrate that the proposed method achieves significant speed up and an accuracy comparable with the brute force Nearest Neighbor method. In addition, a graph cut based clustering technique is employed to demonstrate that the pairwise separability of these rejection classifiers is capable of semantic grouping.

Systematic delay-driven power optimisation and power-driven delay optimisation of combinational circuits

With the proliferation of mobile wireless communication and embedded systems, the energy efficiency becomes a major design constraint. The dissipated energy is often referred as the product of power dissipation and the input-output delay. Most of electronic design automation techniques focus on optimising only one of these parameters either power or delay. Industry standard design flows integrate systematic methods of optimising either area or timing while for power consumption optimisation one often employs heuristics which are characteristic to a specific design. In this work we answer three questions in our quest to provide a systematic approach to joint power and delay Optimisation. The first question of our research is: How to build a design flow which incorporates academic and industry standard design flows for power optimisation? To address this question, we use a reference design flow provided by Synopsys and integrate in this flow academic tools and methodologies. The proposed design flow is used as a platform for analysing some novel algorithms and methodologies for optimisation in the context of digital circuits. The second question we answer is: Is possible to apply a systematic approach for power optimisation in the context of combinational digital circuits? The starting point is a selection of a suitable data structure which can easily incorporate information about delay, power, area and which then allows optimisation algorithms to be applied. In particular we address the implications of a systematic power optimisation methodologies and the potential degradation of other (often conflicting) parameters such as area or the delay of implementation. Finally, the third question which this thesis attempts to answer is: Is there a systematic approach for multi-objective optimisation of delay and power? A delay-driven power and power-driven delay optimisation is proposed in order to have balanced delay and power values. This implies that each power optimisation step is not only constrained by the decrease in power but also the increase in delay. Similarly, each delay optimisation step is not only governed with the decrease in delay but also the increase in power. The goal is to obtain multi-objective optimisation of digital circuits where the two conflicting objectives are power and delay. The logic synthesis and optimisation methodology is based on AND-Inverter Graphs (AIGs) which represent the functionality of the circuit. The switching activities and arrival times of circuit nodes are annotated onto an AND-Inverter Graph under the zero and a non-zero-delay model. We introduce then several reordering rules which are applied on the AIG nodes to minimise switching power or longest path delay of the circuit at the pre-technology mapping level. The academic Electronic Design Automation (EDA) tool ABC is used for the manipulation of AND-Inverter Graphs. We have implemented various combinatorial optimisation algorithms often used in Electronic Design Automation such as Simulated Annealing and Uniform Cost Search Algorithm. Simulated Annealing (SMA) is a probabilistic meta heuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. We used SMA to probabilistically decide between moving from one optimised solution to another such that the dynamic power is optimised under given delay constraints and the delay is optimised under given power constraints. A good approximation to the global optimum solution of energy constraint is obtained. Uniform Cost Search (UCS) is a tree search algorithm used for traversing or searching a weighted tree, tree structure, or graph. We have used Uniform Cost Search Algorithm to search within the AIG network, a specific AIG node order for the reordering rules application. After the reordering rules application, the AIG network is mapped to an AIG netlist using specific library cells. Our approach combines network re-structuring, AIG nodes reordering, dynamic power and longest path delay estimation and optimisation and finally technology mapping to an AIG netlist. A set of MCNC Benchmark circuits and large combinational circuits up to 100,000 gates have been used to validate our methodology. Comparisons for power and delay optimisation are made with the best synthesis scripts used in ABC. Reduction of 23% in power and 15% in delay with minimal overhead is achieved, compared to the best known ABC results. Also, our approach is also implemented on a number of processors with combinational and sequential components and significant savings are achieved.

Integration of micro- and macroscopic models for pedestrian evacuation simulation

Simulation of pedestrian evacuations of smart buildings in emergency is a powerful tool for building analysis, dynamic evacuation planning and real-time response to the evolving state of evacuations. Macroscopic pedestrian models are low-complexity models that are and well suited to algorithmic analysis and planning, but are quite abstract. Microscopic simulation models allow for a high level of simulation detail but can be computationally intensive. By combining micro- and macro- models we can use each to overcome the shortcomings of the other and enable new capability and applications for pedestrian evacuation simulation that would not be possible with either alone. We develop the EvacSim multi-agent pedestrian simulator and procedurally generate macroscopic flow graph models of building space, integrating micro- and macroscopic approaches to simulation of the same emergency space. By “coupling” flow graph parameters to microscopic simulation results, the graph model captures some of the higher detail and fidelity of the complex microscopic simulation model. The coupled flow graph is used for analysis and prediction of the movement of pedestrians in the microscopic simulation, and investigate the performance of dynamic evacuation planning in simulated emergencies using a variety of strategies for allocation of macroscopic evacuation routes to microscopic pedestrian agents. The predictive capability of the coupled flow graph is exploited for the decomposition of microscopic simulation space into multiple future states in a scalable manner. By simulating multiple future states of the emergency in short time frames, this enables sensing strategy based on simulation scenario pattern matching which we show to achieve fast scenario matching, enabling rich, real-time feedback in emergencies in buildings with meagre sensing capabilities.

Sorting under partial information (without the ellipsoid algorithm)

We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to discovering an unknown linear extension of P, using pairwise comparisons. The information-theoretic lower bound on the number of comparisons needed in the worst case is log e(P), the binary logarithm of the number of linear extensions of P. In a breakthrough paper, Jeff Kahn and Jeong Han Kim (STOC 1992) showed that there exists a polynomial-time algorithm for the problem achieving this bound up to a constant factor. Their algorithm invokes the ellipsoid algorithm at each iteration for determining the next comparison, making it impractical. We develop efficient algorithms for sorting under partial information. Like Kahn and Kim, our approach relies on graph entropy. However, our algorithms differ in essential ways from theirs. Rather than resorting to convex programming for computing the entropy, we approximate the entropy, or make sure it is computed only once in a restricted class of graphs, permitting the use of a simpler algorithm. Specifically, we present: an O(n2) algorithm performing O(log n·log e(P)) comparisons; an O(n2.5) algorithm performing at most (1+ε) log e(P) + Oε(n) comparisons; an O(n2.5) algorithm performing O(log e(P)) comparisons. All our algorithms are simple to implement. © 2010 ACM.