Deterministic broadcasting in ad hoc radio networks

We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes know neither the topology nor the size of the network, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. Such networks are called ad hoc multi-hop networks. We study the time of deterministic broadcasting under this scenario. For the model without collision detection, we develop a linear-time broadcasting algorithm for symmetric graphs, which is optimal, and an algorithm for arbitrary n-node graphs, working in time . Next we show that broadcasting with acknowledgement is not possible in this model at all. For the model with collision detection, we develop efficient algorithms for broadcasting and for acknowledged broadcasting in strongly connected graphs. Received: January 2000 / Accepted: June 2001     

NBgossip: An Energy-Efficient Gossip Algorithm for Wireless Sensor Networks

Gossip-based algorithms for information dissemination have recently received significant attention for sensor and ad hoc network applications because of their simplicity and robustness.However,a common drawback of many gossip- based protocols is the waste of energy in passing redundant information over the network.Thus gossip algorithms need to be re-engineered in order to become applicable to energy constrained networks.In this paper,we consider a scenario where each node in the network holds a piece of information(message)at the beginning,and the objective is to simultaneously disseminate all information(messages)among all nodes quickly and cheaply.To provide a practical solution to this problem for ad hoc and sensor networks,NBgossip algorithm is proposed,which is based on network coding and neighborhood gossip. In NBgossip,nodes do not simply forward messages they receive,instead,the linear combinations of the messages are sent out.In addition,every node exchanges messages with its neighboring nodes only.Mathematical proof and simulation studies show that the proposed NBgossip terminates in the optimal O(n)-order rounds and outperforms the existing gossip-based approaches in terms of energy consumption incurred in spreading all the information.     

Asynchronous resource discovery in peer-to-peer networks

The resource discovery problem arises in the context of peer to peer (P2P) networks, where at any point of time a peer may be placed at or removed from any location over a general purpose network (e.g., an Internet site). A node (peer) can communicate with another node directly if and only if it knows a certain routing information to that other node. Hence, a critical task is for the peers to convey this routing information to each other.The problem was formalized by Harchol-Balter et al. and the specific P2P application they had in mind was the logical networks G₀ of servers placed by Akamai at various Internet sites. The routing information needed for a node to reach another peer is that peer’s identifier (e.g., IP address). A logical directed edge represents the fact that the peer at the tail of the edge knows the IP address of the one at its head. The problem is to compute the connected components in the underlying graph of G₀ (namely, the undirected graph obtained from G₀ by removing edge directionality). A number of algorithms were developed in Harchol-Balter et al. for this problem in the model of a synchronous network over a weakly connected directed graph. That is, the assumption was that some clock delivers pulses to every node every time unit at the same time, and a message delivery takes one time unit. The best of these algorithms was randomized. Subsequently, a deterministic algorithm for the problem on synchronous networks with improved complexity was presented in a paper by Kutten et al.The current paper extends the deterministic algorithm of Kutten et al. to the environment of asynchronous networks, where no clock pulses are assumed, and the message delivery time may vary and is not known. We managed to maintain complexities similar to those of the synchronous algorithm of Kutten et al. (translated to the asynchronous model). These are lower than the complexities that would be needed to synchronize the system. The main technical difficulty in a directed, weakly connected system is to ensure that nodes take steps that are consistent with each other, even if their knowledge about each other is not symmetric. Here, this task is further complicated by the fact that there is no timeout mechanism (which does exist in synchronous systems) to assist in ensuring consistency. In particular, as opposed to the case in synchronous systems, an asynchronous algorithm cannot first transform every directed edge to be bidirectional and second, apply an algorithm for bidirectional graph. Thus, our result takes another step towards representing the actual setting in a realistic manner.     

Edge Sums Of De Bruijn Interconnection Networks

An interconnection network is a highly symmetrical connected graph of order n nodes, size m edges, connectivity κ and diameter d , where n and κ are large but m and d are small. Many interconnection networks are defined algebraically in such a way that each node has an integer value. Then every edge can be assigned the sum of the two nodes it joins. These numbers are called the edge sums of the graph. The edge sum problem of a graph is to characterize the set of edge sums. This problem was introduced by Graham and Harary who presented the solution for hypercubes. Our object is to characterize the edge sums for another family of interconnection networks, namely, deBruijn graphs.     

An efficient distributed algorithm for constructing small dominating sets

The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NP-complete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the well-known logarithmic approximation result for the closely related set cover problem. We describe and analyze new randomized distributed algorithms for the dominating set problem that run in polylogarithmic time, independent of the diameter of the network, and that return a dominating set of size within a logarithmic factor from optimal, with high probability. In particular, our best algorithm runs in rounds with high probability, where n is the number of nodes, is one plus the maximum degree of any node, and each round involves a constant number of message exchanges among any two neighbors; the size of the dominating set obtained is within of the optimal in expectation and within of the optimal with high probability. We also describe generalizations to the weighted case and the case of multiple covering requirements. Received: January 2002 / Accepted: August 2002 RID="*" ID="*" Supported by NSF CAREER award NSF CCR-9983901 RID="*" ID="*" Supported by NSF CAREER award NSF CCR-9983901     

A Gossip-Based Energy Conservation Protocol for Wireless Ad Hoc and Sensor Networks

In this paper, we present an energy conservation scheme for wireless ad hoc and sensor networks using gossiping to place nodes in an energy saving sleep state. The technique is termed the Gossip-based Sleep Protocol (GSP). With GSP, each node randomly goes to sleep for some time with gossip sleep probability p. GSP is based on the observation that in a well connected network there are usually many paths between a source and destination, so a percentage of nodes can be in an energy conserving sleep mode without losing network connectivity. GSP needs few operations, scales to large networks and does not require a wireless node to maintain the states of other nodes. We propose two versions of GSP, one for synchronous networks and one for asynchronous networks, and afterward extend GSP to adapt to network traffic conditions. We show the advantages of the GSP approach through both simulations and analysis.     

Synchronous bandwidth allocation in FDDI networks

It is well known that an FDDI token ring network provides a guaranteed throughput for synchronous messages and a bounded medium access delay for each node/station. However, this fact alone cannot effectively support many real-time applications that require the timely delivery of each critical message. The reason for this is that the FDDI guarantees a medium access delay bound to nodes, but not to messages themselves. The message-delivery delays may exceed the medium-access delay bound even if a node transmits synchronous messages at a rate not greater than the guaranteed throughput. We solve this problem by developing a synchronous bandwidth allocation (SEA) scheme which calculates the synchronous bandwidth necessary for each application to satisfy its message-delivery delay requirement. The result obtained in this paper is essential for effective use of the FDDI token ring networks in supporting such real-time communication as digital video/audio transmissions, and distributed control/monitoring     

Mean-field framework for performance evaluation of push-pull gossip protocols

Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done using simulations, but these tend to be expensive in computation time and memory consumption.We employ mean-field analysis techniques for the evaluation of gossip protocols. Nodes in the network are represented by small identical stochastic processes. Joining all nodes would result in an enormous stochastic process. If the number of nodes goes to infinity, however, mean-field analysis allows us to replace this intractably large stochastic process by a small deterministic process. This process approximates the behaviour of very large gossip networks, and can be evaluated using simple matrix-vector multiplications.     

EDGly: detection of influential nodes using game theory

Identifying those nodes that play a critical role within a network is of great importance. Many applications such as gossip spreading, disease spreading, news dispersion, identifying prominent individuals in a social network, etc. may take advantage of this knowledge in a complex network. The basic concept is generally to identify the nodes with the highest criticality in a network. As a result, the centrality principle has been studied extensively and in great detail, focusing on creating a consistent and accurate location of nodes within a network in terms of their importance. Both single centrality measures and group centrality measures, although, have their certain drawbacks. Other solutions to this problem include the game-theoretic Shapley Value (SV) calculations measuring the effect of a collection of nodes in complex networks via dynamic network data propagation process. Our novel proposed algorithm aims to find the most significant communities in a graph with community structure and then employs the SV-based games to find the most influential node from each community. A Susceptible-Infected-Recovered (SIR) model has been employed to distinctly determine each powerful node's capacity to spread. The results of the SIR simulation have also been used to show the contrast between the spreading capacity of nodes found through our proposed algorithm and that of nodes found using SV-algorithm and centrality measures alone.

     

Discovering Network Topology in the Presence of Byzantine Faults

We pose and study the problem of Byzantine-robust topology discovery in an arbitrary asynchronous network. The problem is an abstraction of fault-tolerant routing. We formally state the weak and strong versions of the problem. The weak version requires that either each node discovers the topology of the network or at least one node detects the presence of a faulty node. The strong version requires that each node discovers the topology regardless of faults. We focus on noncryptographic solutions to these problems. We explore their bounds. We prove that the weak topology discovery problem is solvable only if the connectivity of the network exceeds the number of faults in the system. Similarly, we show that the strong version of the problem is solvable only if the network connectivity is more than twice the number of faults. We present solutions to both versions of the problem. The presented algorithms match the established graph connectivity bounds. The algorithms do not require the individual nodes to know either the diameter or the size of the network. The message complexity of both programs is low polynomial with respect to the network size. We describe how our solutions can be extended to add the property of termination, handle topology changes, and perform neighborhood discovery.     

Long-lived Rambo: Trading knowledge for communication

Shareable data services providing consistency guarantees, such as atomicity (linearizability), make building distributed systems easier. However, combining linearizability with efficiency in practical algorithms is difficult. A reconfigurable linearizable data service, called Rambo, was developed by Lynch and Shvartsman. This service guarantees consistency under dynamic conditions involving asynchrony, message loss, node crashes, and new node arrivals. The specification of the original algorithm is given at an abstract level aimed at concise presentation and formal reasoning about correctness. The algorithm propagates information by means of gossip messages. If the service is in use for a long time, the size and the number of gossip messages may grow without bound. This paper presents a consistent data service for long-lived objects that improves on Rambo in two ways: it includes an incremental communication protocol and a leave service. The new protocol takes advantage of the local knowledge, and carefully manages the size of messages by removing redundant information, while the leave service allows the nodes to leave the system gracefully. The new algorithm is formally proved correct by forward simulation using levels of abstraction. An experimental implementation of the system was developed for networks-of-workstations. The paper also includes selected analytical and preliminary empirical results that illustrate the advantages of the new algorithm.     

On the complexity of distributed stable matching with small messages

We consider the distributed complexity of the stable matching problem (a.k.a. “stable marriage”). In this problem, the communication graph is undirected and bipartite, and each node ranks its neighbors. Given a matching of the nodes, a pair of unmatched nodes is called blocking if they prefer each other to their assigned match. A matching is called stable if it does not induce any blocking pair. In the distributed model, nodes exchange messages in each round over the communication links, until they find a stable matching. We show that if messages may contain at most B bits each, then any distributed algorithm that solves the stable matching problem requires ${\Omega(\sqrt{n/B\log n})}We consider the distributed complexity of the stable matching problem (a.k.a. “stable marriage”). In this problem, the communication graph is undirected and bipartite, and each node ranks its neighbors. Given a matching of the nodes, a pair of unmatched nodes is called blocking if they prefer each other to their assigned match. A matching is called stable if it does not induce any blocking pair. In the distributed model, nodes exchange messages in each round over the communication links, until they find a stable matching. We show that if messages may contain at most B bits each, then any distributed algorithm that solves the stable matching problem requires W(?{n/Blogn}){\Omega(\sqrt{n/B\log n})} communication rounds in the worst case, even for graphs of diameter O(log n), where n is the number of nodes in the graph. Furthermore, the lower bound holds even if we allow the output to contain O(?n){O(\sqrt n)} blocking pairs, and if a pair is considered blocking only if they like each other much more then their assigned match.     

A novel gossip-based sensing coverage algorithm for dense wireless sensor networks

Wireless sensor networks (WSNs) have been widely studied and usefully employed in many applications such as monitoring environments and embedded systems. WSNs consist of many nodes spread randomly over a wide area; therefore, the sensing regions of different nodes may overlap partially. This is called the “sensing coverage problem”. In this paper, we define a maximum sensing coverage region (MSCR) problem and present a novel gossip-based sensing-coverage-aware algorithm to solve the problem. In the algorithm, sensor nodes gossip with their neighbors about their sensing coverage region. In this way, nodes decide locally to forward packets (as an active node) or to disregard packets (as a sleeping or redundant node). Being sensing-coverage-aware, the redundant node can cut back on its activities whenever its sensing region is k-covered by enough neighbors. With the distributed and low-overhead traffic benefits of gossip, we spread energy consumption to different sensor nodes, achieve maximum sensing coverage with minimal energy consumption in each individual sensor node, and prolong the whole network lifetime. We apply our algorithm to improve LEACH, a clustering routing protocol for WSNs, and develop a simulation to evaluate the performance of the algorithm.     

Centralized asynchronous broadcast in radio networks

We study asynchronous broadcasting in packet radio networks. A radio network is represented by a directed graph, in which one distinguished source node stores a message that needs to be disseminated among all the remaining nodes. An asynchronous execution of a protocol is a sequence of events, each consisting of simultaneous deliveries of messages. The correctness of protocols is considered for specific adversarial models defined by restrictions on events the adversary may schedule. A protocol specifies how many times the source message is to be retransmitted by each node. The total number of transmissions over all the nodes is called the work of the broadcast protocol; it is used as complexity measure. We study computational problems, to be solved by deterministic centralized algorithms, either to find a broadcast protocol or to verify the correctness of a protocol, for a given network. The amount of work necessary to make a protocol correct may have to be exponential in the size of network. There is a polynomial-time algorithm to find a broadcast protocol for a given network. We show that certain problems about broadcasting protocols for given networks are complete in NP and co-NP complexity classes.     

Modeling and navigation of social information networks in metric spaces

We are living in a world of various kinds of social information networks with small-world and scale-free characteristics. It is still an intriguing problem for researchers to explain how and why so many obviously different networks emerge and share common intrinsic characteristics such as short diameter, higher cluster and power-law degree distribution. Most previous works studied the topology formation and information navigation of complex networks in separated models. In this paper, we propose a metric based range intersection model to explore the topology evolution and information navigation in a synthetic way. We model the network as a set of nodes in a distance metric space where each node has an ID and a range of neighbor information around its ID in the metric space. The range of a node can be seen as the local knowledge or information that the node has around its position in the metric space. The topology is formed by setting up a link between two nodes that have intersected ranges. Information navigation over the network is modeled as a greedy routing process using neighbor links and the distance metric. Different from previous models, we do not assume that nodes join the network one by one and set up link according to the degree distribution of existing nodes or distances between nodes. Range of node is the key factor determining the topology and navigation properties of a network. Moreover, as the ranges of nodes grow, the network evolves from a set of totally isolated nodes to a connected network. Thus, we can easily model the network evolutions in terms of the network size and the individual node information range using the range intersection model. A set of experiments shows that networks constructed using the range intersection model have the scale-free degree distribution, high cluster, short diameter, and high navigability properties that are owned by the real networks.     

Leapfrog: Optimal Opportunistic Routing in Probabilistically Contacted Delay Tolerant Networks

Delay tolerant networks (DTNs) experience frequent and long lasting network disconnection due to various reasons such as mobility, power management, and scheduling. One primary concern in DTNs is to route messages to keep the end-to-end delivery delay as low as possible. In this paper, we study the single-copy message routing problem and propose an optimal opportunistic routing strategy – Leapfrog Routing – for probabilistically contacted DTNs where nodes encounter or contact in some fixed probabilities. We deduce the iterative computation formulate of minimum expected opportunistic delivery delay from each node to the destination, and discover that under the optimal opportunistic routing strategy, messages would be delivered from high-delay node to low-delay node in the leapfrog manner. Rigorous theoretical analysis shows that such a routing strategy is exactly the optimal among all possible ones. Moreover, we apply the idea of Reverse Dijkstra algorithm to design an algorithm. When a destination is given, this algorithm can determine for each node the routing selection function under the Leapfrog Routing strategy. The computation overhead of this algorithm is only O(n ²) where n is the number of nodes in the network. In addition, through extensive simulations based on real DTN traces, we demonstrate that our algorithm can significantly outperform the previous ones.     

Deterministic broadcasting time with partial knowledge of the network

We consider the time of deterministic broadcasting in networks whose nodes have limited knowledge of network topology. Each node v knows only the part of the network within knowledge radius r from it, i.e., it knows the graph induced by all nodes at distance at most r from v. Apart from that, each node knows the maximum degree Δ of the network. One node of the network, called the source, has a message which has to reach all other nodes. We adopt the widely studied communication model called the one-way model in which, in every round, each node can communicate with at most one neighbor, and in each pair of nodes communicating in a given round, one can only send a message while the other can only receive it. This is the weakest of all store-and-forward models for point-to-point networks, and hence our algorithms work for other models as well, in at most the same time.

We show trade-offs between knowledge radius and time of deterministic broadcasting, when the knowledge radius is small, i.e., when nodes are only aware of their close vicinity. While for knowledge radius 0, minimum broadcasting time is Θ(e), where e is the number of edges in the network, broadcasting can be usually completed faster for positive knowledge radius. Our main results concern knowledge radius 1. We develop fast broadcasting algorithms and analyze their execution time. We also prove lower bounds on broadcasting time, showing that our algorithms are close to optimal.     

Clustered maximum weight clique problem: Algorithms and empirical analysis

We introduce the Clustered Maximum Weight Clique Problem (CCP), a generalization of the Maximum Weight Clique Problem, that models an image acquisition scheduling problem for a satellite constellation. The solution of CCP represents satellite schedules that satisfy customer requests for satellite imagery. Each request has a priority, an area of interest, and a time window. Often, the area of interest is too large to be imaged by one satellite pass and it has to be divided into several smaller images. Each image has one or more opportunities for an acquisition by a satellite.The problem is modeled by a clustered weighted graph. A graph node represents one opportunity for an image acquisition by one satellite. A graph edge indicates that either two opportunities are not in conflict – can both be in a schedule, or two opportunities are not acquiring the same image. Each graph node has a weight that represents the area size of the image. The graph nodes are partitioned into clusters each of which encompasses all the opportunities of one customer request. The priority of the request is captured by the cluster weight. The time window of the request restricts the number of opportunities.The CCP deals with finding a clique of a maximum weight where the weight combines the node weights and the cluster weights. More precisely, the cluster weight is multiplied by the contribution of the sum of the weights of the clique nodes. The contribution is either a linear function or a piece-wise linear function, where the latter is meant to favour finalizing an already partially served customer request.The paper presents several mathematical programming formulations of the CCP and proposes matheuristic solution approaches. The computational study is performed on the clustered adaptations of the DIMACS and BHOSLIB benchmark instances for the Maximum Weight Clique Problem. The achieved results are encouraging.     

GLEAM: a graph clustering framework based on potential game optimization for large-scale social networks

With the growing explosion of online social networks, the study of large-scale graph clustering has attracted considerable interest. Most of traditional methods view the graph clustering problem as an optimization problem based on a given objective function; however, there are few methodical theories for the emergence of clusters over real-life networks. In this paper, each actor in online social networks is viewed as a selfish player in a non-cooperative game. The strategy associated with each node is defined as the cluster membership vector, and each one’s incentive is to maximize its own social identity by adopting the most suitable strategy. The definition of utility function in our game model is inspired by the conformity psychology, which is defined as the weighted average of one’s social identity by participating different clusters. With this setting, the proposed game can well match a potential game. So that the cluster could be shaped by the actions of those closely interactive users who adopt the same strategy in a Nash equilibrium. To this end, we propose a novel Graph cLustering framework based on potEntial gAme optiMization (GLEAM) for parallel graph clustering. It first utilize the cosine similarity to weight each edge in the original network. Then, an initial partition, including a number of clusters dominated by those potential “leader nodes”, is created by a fast heuristic process. Third, a potential game-based weighted Modularity optimization is used to improve the initial partition. Finally, we introduce the notion of potentially attractive cluster, and then discover the overlapping partition of the graph using a simple double-threshold procedure. Three phases in GLEAM are carefully designed for parallel execution. Experiments on real-world networks analyze the convergence inside GLEAM, and demonstrate the high performance of GLEAM by comparing it with the state-of-the-art community detection approaches in the literature.     

基于协作推断的正例未标注图学习算法

针对现有正例未标注图学习方法仅提取节点表征信息、独立推断节点类别的问题,提出了一种基于协作推断分类算法,利用节点之间关联信息来帮助推断未标注节点的标签。首先,采用个性化网页排位算法计算每个节点与全体已知正例节点的关联度。其次,采用一个图神经网络学习节点表征信息,与正例关联度联合构造一个局部分类器,预测未标注节点标签;采用另一个图神经网络获取局部节点标签之间依赖关系,与正例关联度联合构造一个关系分类器,协作更新未标注节点标签。然后,借鉴马尔可夫图神经网络方法交替迭代地训练两者,形成多跳步节点标签之间的协作推断;并且,为有效利用正例与未标注节点训练分类器,提出了混合非负无偏风险评估函数。最后,选择两者中任意一个,预测未标注节点的类别。在真实数据集上的实验结果表明,无论是识别单类别正例还是识别多类别合成正例,所述算法均表现出比其他正例未标注学习方法更佳效果,且对正例先验概率误差表现出更好的鲁棒性。