This is a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.

Intermittently connected mobile networks are sparse wireless networks where most of the time there does not exist a complete path from the source to the destination. These networks

Abstract — This paper presents and analyzes an architecture that exploits the serendipitous movement of mobile agents in an environment to collect sensor data in sparse sensor networks. The mobile entities, called MULEs, pick up data from sensors when in close range, buffer it, and drop off the data to wired access points when in proximity. This leads to substantial power savings at the sensors as they only have to transmit over a short range. Detailed performance analysis is presented based on a simple model of the system incorporating key system variables such as number of MULEs, sensors and access points. The performance metrics observed are the data success rate (the fraction of generated data that reaches the access points) and the required buffer capacities on the sensors and the MULEs. The modeling along with simulation results can be used for further analysis and provide certain guidelines for deployment of such systems. I.

between computers, and a resulting paradigm shift from centralized to highly distributed systems. With massive scale also comes massive instability, as node and link failures become the norm rather than the exception. For such highly volatile systems, decentralized gossip-based protocols are emerging as an approach to maintaining simplicity and scalability while achieving fault-tolerant information dissemination.

Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from the source to the destination. There are many real networks that follow this model, for example, wildlife tracking sensor networks, military networks, vehicular ad hoc networks, etc. In this context, conventional routing schemes fail, because they try to establish complete end-to-end paths, before any data is sent. To deal with such networks researchers have suggested to use flooding-based routing schemes. While flooding-based schemes have a high probability of delivery, they waste a lot of energy and suffer from severe contention which can significantly degrade their performance. Furthermore, proposed efforts to reduce the overhead of flooding-based schemes have often been plagued by large delays. With this in mind, we introduce a new family of routing schemes that “spray ” a few message copies into the network, and then route each copy independently towards the destination. We show that, if carefully designed, spray routing not only performs significantly fewer transmissions per message, but also has lower average delivery delays than existing schemes; furthermore, it is highly scalable and retains good performance under a large range of scenarios. Finally, we use our theoretical framework proposed in our 2004 paper to analyze the performance of spray routing. We also use this theory to show how to choose the number of copies to be sprayed and how to optimally distribute these copies to relays.

We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. For searching, we argue that random walks achieve improvement over flooding in the case of clustered overlay topologies and in the case of re-issuing the same request several times. For construction, we argue that an expander can be maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk can achieve statistical properties similar to independent sampling (if the second eigenvalue of the transition matrix is bounded away from 1, which translates to good expansion of the network; such connectivity is desired, and believed to hold, in every reasonable network and network model). This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.

Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn 2) and space O(n 2) in the worst case, and in time O(n 2 log n) and space O(n 2) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.

View an n-vertex, m-edge undirected graph as an electrical network with unit resistors as edges. We extend known relations between random walks and electrical networks by showing that resistance in this network is intimately connected with the lengths of random walks on the graph. For example, the commute time between two vertices s and t (the expected length of a random walk from s to t and back) is precisely characterized by the e ective resistance Rst between s and t: commute time = 2mRst. As a corollary, the cover time (the expected length of a random walk visiting all vertices) is characterized by the maximum resistance R in the graph to within a factor of log n: mR cover time O(mR log n). For many graphs, the bounds on cover time obtained in this manner are better than those obtained from previous techniques such as the eigenvalues of the adjacency matrix. In particular, we improve known bounds on cover times for high-degree graphs and expanders, and give new proofs of known results for multidimensional meshes. Moreover, resistance seems to provide an intuitively appealing and tractable approach to these problems.

This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions. 1. Overview Ever since the discovery of quantum mechanics people have been puzzled by the counter-intuitive character of the laws of nature. Over time we have learned to accept more and more effects that are unimaginable in a classical Newtonian world. Modern technology exploits quantum effects both to our benefit and detriment—among the memorable examples we should cite laser technology and not omit the atomic bomb. In recent years interest in quantum information theory has been generated by the prospect of employing its laws to design devices of surprising power [1]. New ideas include quantum cryptography [2, 3] and quantum computation. In 1994 Shor [4] discovered a quantum algorithm to factor numbers efficiently (that is in time that grows only polynomically with the length of the number to be factored). This has unleashed a wave of activity across a broad range of disciplines: physics, computer science, mathematics and engineering. This fruitful axis of research has uncovered many new effects that are strikingly different from their classical counterparts, both from the physical point of view as well as from a computer science and communication theory perspective. Over time these communities have gained a greater understanding of the concepts and notions of the other. The idea that information cannot be separated from

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