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.

Preferential Field Coverage Through Detour-Based Mobility Coordination

Controlling the mobility pattern of mobile nodes (e.g., robots) to monitor a given field is a well-studied problem in sensor networks. In this setup, absolute control over the nodes’ mobility is assumed. Apart from the physical ones, no other constraints are imposed on planning mobility of these nodes. In this paper, we address a more general version of the problem. Specifically, we consider a setting in which mobility of each node is externally constrained by a schedule consisting of a list of locations that the node must visit at particular times. Typically, such schedules exhibit some level of slack, which could be leveraged to achieve a specific coverage distribution of a field. Such a distribution defines the relative importance of different field locations. We define the Constrained Mobility Coordination problem for Preferential Coverage (CMC-PC) as follows: given a field with a desired monitoring distribution, and a number of nodes n, each with its own schedule, we need to coordinate the mobility of the nodes in order to achieve the following two goals: 1) satisfy the schedules of all nodes, and 2) attain the required coverage of the given field. We show that the CMC-PC problem is NP-complete (by reduction to the Hamiltonian Cycle problem). Then we propose TFM, a distributed heuristic to achieve field coverage that is as close as possible to the required coverage distribution. We verify the premise of TFM using extensive simulations, as well as taxi logs from a major metropolitan area. We compare TFM to the random mobility strategy—the latter provides a lower bound on performance. Our results show that TFM is very successful in matching the required field coverage distribution, and that it provides, at least, two-fold query success ratio for queries that follow the target coverage distribution of the field.

PreDA: Predicate Routing for DTN Architectures over MANET

We consider a Delay Tolerant Network (DTN) whose users (nodes) are connected by an underlying Mobile Ad hoc Network (MANET) substrate. Users can declaratively express high-level policy constraints on how “content” should be routed. For example, content can be directed through an intermediary DTN node for the purposes of preprocessing, authentication, etc., or content from a malicious MANET node can be dropped. To support such content routing at the DTN level, we implement Predicate Routing [1] where high-level constraints of DTN nodes are mapped into low-level routing predicates within the MANET nodes. Our testbed [2] uses a Linux system architecture with User Mode Linux [3] to emulate every DTN node with a DTN Reference Implementation code [4]. In our initial architecture prototype, we use the On Demand Distance Vector (AODV) routing protocol at the MANET level. We use the network simulator ns-2 (ns-emulation version) to simulate the wireless connectivity of both DTN and MANET nodes. Preliminary results show the efficient and correct operation of propagating routing predicates. For the application of content re-routing through an intermediary, as a side effect, results demonstrate the performance benefit of content re-routing that dynamically (on-demand) breaks the underlying end-to-end TCP connections into shorter-length TCP connections.

Principles of Safe Policy Routing Dynamics

We introduce the Dynamic Policy Routing (DPR) model that captures the propagation of route updates under arbitrary changes in topology or path preferences. DPR introduces the notion of causation chains where the route flap at one node causes a flap at the next node along the chain. Using DPR, we model the Gao-Rexford (economic) guidelines that guarantee the safety (i.e., convergence) of policy routing. We establish three principles of safe policy routing dynamics. The non-interference principle provides insight into which ASes can directly induce route changes in one another. The single cycle principle and the multi-tiered cycle principle provide insight into how cycles of routing updates can manifest in any network. We develop INTERFERENCEBEAT, a distributed algorithm that propagates a small token along causation chains to check adherence to these principles. To enhance the diagnosis power of INTERFERENCEBEAT, we model four violations of the Gao-Rexford guidelines (e.g., transiting between peers) and characterize the resulting dynamics.

Object Matching in Distributed Video Surveillance Systems by LDA-Based Appearance Descriptors

Establishing correspondences among object instances is still challenging in multi-camera surveillance systems, especially when the cameras’ fields of view are non-overlapping. Spatiotemporal constraints can help in solving the correspondence problem but still leave a wide margin of uncertainty. One way to reduce this uncertainty is to use appearance information about the moving objects in the site. In this paper we present the preliminary results of a new method that can capture salient appearance characteristics at each camera node in the network. A Latent Dirichlet Allocation (LDA) model is created and maintained at each node in the camera network. Each object is encoded in terms of the LDA bag-of-words model for appearance. The encoded appearance is then used to establish probable matching across cameras. Preliminary experiments are conducted on a dataset of 20 individuals and comparison against Madden’s I-MCHR is reported.

On the Cost of Supporting Multihoming and Mobility

As the Internet has evolved and grown, an increasing number of nodes (hosts or autonomous systems) have become multihomed, i.e., a node is connected to more than one network. Mobility can be viewed as a special case of multihoming—as a node moves, it unsubscribes from one network and subscribes to another, which is akin to one interface becoming inactive and another active. The current Internet architecture has been facing significant challenges in effectively dealing with multihoming (and consequently mobility). The Recursive INternet Architecture (RINA) [1] was recently proposed as a clean-slate solution to the current problems of the Internet. In this paper, we perform an average-case cost analysis to compare the multihoming / mobility support of RINA, against that of other approaches such as LISP and MobileIP. We also validate our analysis using trace-driven simulation.

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.

Angels: In-Network Support for Minimum Distribution Time in P2P Overlays

This thesis proposes the use of in-network caches (which we call Angels) to reduce the Minimum Distribution Time (MDT) of a file from a seeder – a node that possesses the file – to a set of leechers – nodes who are interested in downloading the file. An Angel is not a leecher in the sense that it is not interested in receiving the entire file, but rather it is interested in minimizing the MDT to all leechers, and as such uses its storage and up/down-link capacity to cache and forward parts of the file to other peers. We extend the analytical results by Kumar and Ross (Kumar and Ross, 2006) to account for the presence of angels by deriving a new lower bound for the MDT. We show that this newly derived lower bound is tight by proposing a distribution strategy under assumptions of a fluid model. We present a GroupTree heuristic that addresses the impracticalities of the fluid model. We evaluate our designs through simulations that show that our GroupTree heuristic outperforms other heuristics, that it scales well with the increase of the number of leechers, and that it closely approaches the optimal theoretical bounds.

Distributed Packet Rewriting and its Application to Scalable Server Architectures

To construct high performance Web servers, system builders are increasingly turning to distributed designs. An important challenge that arises in distributed Web servers is the need to direct incoming connections to individual hosts. Previous methods for connection routing have employed a centralized node which handles all incoming requests. In contrast, we propose a distributed approach, called Distributed Packet Rewriting (DPR), in which all hosts of the distributed system participate in connection routing. We argue that this approach promises better scalability and fault-tolerance than the centralized approach. We describe our implementation of four variants of DPR and compare their performance. We show that DPR provides performance comparable to centralized alternatives, measured in terms of throughput and delay under the SPECweb96 benchmark. Finally, we argue that DPR is particularly attractive both for small scale systems and for systems following the emerging trend toward increasingly intelligent I/O subsystems.

On the Origin of Power Laws in Internet Topologies

Recent empirical studies have shown that Internet topologies exhibit power laws of the form for the following relationships: (P1) outdegree of node (domain or router) versus rank; (P2) number of nodes versus outdegree; (P3) number of node pairs y = x^α within a neighborhood versus neighborhood size (in hops); and (P4) eigenvalues of the adjacency matrix versus rank. However, causes for the appearance of such power laws have not been convincingly given. In this paper, we examine four factors in the formation of Internet topologies. These factors are (F1) preferential connectivity of a new node to existing nodes; (F2) incremental growth of the network; (F3) distribution of nodes in space; and (F4) locality of edge connections. In synthetically generated network topologies, we study the relevance of each factor in causing the aforementioned power laws as well as other properties, namely diameter, average path length and clustering coefficient. Different kinds of network topologies are generated: (T1) topologies generated using our parametrized generator, we call BRITE; (T2) random topologies generated using the well-known Waxman model; (T3) Transit-Stub topologies generated using GT-ITM tool; and (T4) regular grid topologies. We observe that some generated topologies may not obey power laws P1 and P2. Thus, the existence of these power laws can be used to validate the accuracy of a given tool in generating representative Internet topologies. Power laws P3 and P4 were observed in nearly all considered topologies, but different topologies showed different values of the power exponent α. Thus, while the presence of power laws P3 and P4 do not give strong evidence for the representativeness of a generated topology, the value of α in P3 and P4 can be used as a litmus test for the representativeness of a generated topology. We also find that factors F1 and F2 are the key contributors in our study which provide the resemblance of our generated topologies to that of the Internet.

On the Marginal Utility of Deploying Measurement Infrastructure

The cost and complexity of deploying measurement infrastructure in the Internet for the purpose of analyzing its structure and behavior is considerable. Basic questions about the utility of increasing the number of measurements and/or measurement sites have not yet been addressed which has lead to a "more is better" approach to wide-area measurements. In this paper, we quantify the marginal utility of performing wide-area measurements in the context of Internet topology discovery. We characterize topology in terms of nodes, links, node degree distribution, and end-to-end flows using statistical and information-theoretic techniques. We classify nodes discovered on the routes between a set of 8 sources and 1277 destinations to differentiate nodes which make up the so called "backbone" from those which border the backbone and those on links between the border nodes and destination nodes. This process includes reducing nodes that advertise multiple interfaces to single IP addresses. We show that the utility of adding sources goes down significantly after 2 from the perspective of interface, node, link and node degree discovery. We show that the utility of adding destinations is constant for interfaces, nodes, links and node degree indicating that it is more important to add destinations than sources. Finally, we analyze paths through the backbone and show that shared link distributions approximate a power law indicating that a small number of backbone links in our study are very heavily utilized.

Mistreatment in Distributed Caching Groups: Causes and Implications

Although cooperation generally increases the amount of resources available to a community of nodes, thus improving individual and collective performance, it also allows for the appearance of potential mistreatment problems through the exposition of one node’s resources to others. We study such concerns by considering a group of independent, rational, self-aware nodes that cooperate using on-line caching algorithms, where the exposed resource is the storage of each node. Motivated by content networking applications – including web caching, CDNs, and P2P – this paper extends our previous work on the off-line version of the problem, which was limited to object replication and was conducted under a game-theoretic framework. We identify and investigate two causes of mistreatment: (1) cache state interactions (due to the cooperative servicing of requests) and (2) the adoption of a common scheme for cache replacement/redirection/admission policies. Using analytic models, numerical solutions of these models, as well as simulation experiments, we show that online cooperation schemes using caching are fairly robust to mistreatment caused by state interactions. When this becomes possible, the interaction through the exchange of miss-streams has to be very intense, making it feasible for the mistreated nodes to detect and react to the exploitation. This robustness ceases to exist when nodes fetch and store objects in response to remote requests, i.e., when they operate as Level-2 caches (or proxies) for other nodes. Regarding mistreatment due to a common scheme, we show that this can easily take place when the “outlier” characteristics of some of the nodes get overlooked. This finding underscores the importance of allowing cooperative caching nodes the flexibility of choosing from a diverse set of schemes to fit the peculiarities of individual nodes. To that end, we outline an emulation-based framework for the development of mistreatment-resilient distributed selfish caching schemes.

Distributed Selfish Coaching

Although cooperation generally increases the amount of resources available to a community of nodes, thus improving individual and collective performance, it also allows for the appearance of potential mistreatment problems through the exposition of one node's resources to others. We study such concerns by considering a group of independent, rational, self-aware nodes that cooperate using on-line caching algorithms, where the exposed resource is the storage at each node. Motivated by content networking applications -- including web caching, CDNs, and P2P -- this paper extends our previous work on the on-line version of the problem, which was conducted under a game-theoretic framework, and limited to object replication. We identify and investigate two causes of mistreatment: (1) cache state interactions (due to the cooperative servicing of requests) and (2) the adoption of a common scheme for cache management policies. Using analytic models, numerical solutions of these models, as well as simulation experiments, we show that on-line cooperation schemes using caching are fairly robust to mistreatment caused by state interactions. To appear in a substantial manner, the interaction through the exchange of miss-streams has to be very intense, making it feasible for the mistreated nodes to detect and react to exploitation. This robustness ceases to exist when nodes fetch and store objects in response to remote requests, i.e., when they operate as Level-2 caches (or proxies) for other nodes. Regarding mistreatment due to a common scheme, we show that this can easily take place when the "outlier" characteristics of some of the nodes get overlooked. This finding underscores the importance of allowing cooperative caching nodes the flexibility of choosing from a diverse set of schemes to fit the peculiarities of individual nodes. To that end, we outline an emulation-based framework for the development of mistreatment-resilient distributed selfish caching schemes. Our framework utilizes a simple control-theoretic approach to dynamically parameterize the cache management scheme. We show performance evaluation results that quantify the benefits from instantiating such a framework, which could be substantial under skewed demand profiles.