Memoryless search algorithms in a network with faulty advice

In this paper, we present a randomized algorithm for a mobile agent to search for an item stored at a node t of a network, without prior knowledge of its exact location. Each node of the network has a database that will answer queries of the form “how do I find t?” by responding with the first edge on a shortest path to t. It may happen that some nodes, called liars, give bad advice. We investigate a simple memoryless algorithm which follows the advice with some fixed probability q>1/2 and otherwise chooses a random edge. If the degree of each node and number of liars k are bounded, we show that the expected number of edges traversed by the agent before finding t is bounded from above by O(d+r^k), where d is the distance between the initial and target nodes and . We also show that this expected number of steps can be significantly improved for particular topologies such as the complete graph and the torus.     

Metacube—a versatile family of interconnection networks for extremely large-scale supercomputers

In the next decade, the high-performance supercomputers will consist of several millions of CPUs. The interconnection networks in such supercomputers play an important role for achieving high performance. In this paper, we introduce the Metacube (MC), a versatile family of interconnection network that can connect an extremely large number of nodes with a small number of links per node and keep the diameter rather low. An MC network has a 2-level hypercube structure. An MC(k,m) network can connect 2^2km+k2^{2^{k}m+k} nodes with m+k links per node, where k is the dimension of the high-level hypercubes (classes) and m is the dimension of the low-level hypercubes (clusters). An MC is a symmetric network with short diameter, easy and efficient routing and broadcasting similar to that of the hypercube. However, the MC network can connect millions of nodes with up to 6 links per node. An MC(2,3) with 5 links per node has 16,384 nodes and an MC(3,3) with 6 links per node has 134,217,728 nodes. We describe the MC network’s structure, topological properties, routing and broadcasting algorithms, and the Hamiltonian cycle embedding in the Metacube networks.     

Dynamic Multicast in Overlay Networks with Linear Capacity Constraints

In a peer-to-peer overlay network, the phenomenon of multiple overlay links sharing bottleneck physical links leads to correlation of overlay link capacities. We are able to more accurately model the overlay by incorporating these linear capacity constraints (LCCs). We formulate the problem of maximizing bandwidth in overlay multicast using our LCC model. We show that finding a maximum bandwidth multicast tree in an overlay network with LCC is NP-complete. Therefore, an efficient heuristics algorithm is designed to solve the problem. Extensive simulations show that our algorithm is able to construct multicast trees that are optimal or extremely close to optimal, with significantly higher bandwidth than trees formed in overlays with no LCC. Furthermore, we develop a fully distributed algorithm for obtaining near-optimal multicast trees, by means of gossip-based algorithms and a restricted but inherently distributed class of LCC (node-based LCC). We demonstrate that the distributed algorithm converges quickly to the centralized optimal and is highly scalable.     

Circle formation of weak robots and Lyndon words

In this paper a discrete-time dynamic random graph process is studied that interleaves the birth of nodes and edges with the death of nodes. In this model, at each time step either a new node is added or an existing node is deleted. A node is added with probability p together with an edge incident on it. The node at the other end of this new edge is chosen based on a linear preferential attachment rule. A node (and all the edges incident on it) is deleted with probability q=1−p. The node to be deleted is chosen based on a probability distribution that favors small-degree nodes, in view of recent empirical findings. We analyze the degree distribution of this model and find that the expected fraction of nodes with degree k in the graph generated by this process decreases asymptotically as k−1−(2p/2p−1).     

ACOM: Any-source Capacity-constrained Overlay Multicast in Non-DHT P2P Networks

rdquoApplication-level multicast is a promising alternative to IP multicast due to its independence from the IP routing infrastructure and its flexibility in constructing the delivery trees. The existing overlay multicast systems either support a single data source or have high maintenance overhead when multiple sources are allowed. They are inefficient for applications that require any-source multicast with varied host capacities and dynamic membership. This paper proposes ACOM, an any-source capacity-constrained overlay multicast system, consisting of three distributed multicast algorithms on top of a non-DHT overlay network with simple structures (random overlay with a non-DHT ring) that are easy to manage as nodes join and depart. The nodes have different capacities, and they can support different numbers of direct children during a multicast session. No explicit multicast trees are maintained on top of the overlay. The distributed execution of the algorithms naturally defines an implicit, roughly balanced, capacity-constrained multicast tree for each source node. We prove that the system can deliver a multicast message from any source to all nodes in expected O(log_c n) hops, which is asymptotically optimal, where c is the average node capacity and n is the number of members in a multicast group.     

一种具有能力约束性能的任意源覆盖多播方法

近年来提出的许多面向单个数据源设计的多播树并不能简单扩展到任意源多播系统中,因为针对每个源建立一个树代价高昂.而已存在的一些允许多数据源的P2P(peer-to-peer)系统的维护量大,在体现结点能力差异等方面缺少灵活性.提出一个任意源覆盖多播服务方案,并具有结点能力约束性能.它建立在非DHT(distributed hash table)覆盖网络上,无须建立显式的多播树.设计了两种分布式多播算法,它们将任意源的多播信息传送到所有结点的期望跳数是O(log_cn),其中,c是平均结点能力,n是多播组中的结点个数.     

Modeling gossip-based content dissemination and search in distributed networking

This paper presents a rigorous analytic study of gossip-based message dissemination schemes that can be employed for content/service dissemination or discovery in unstructured and distributed networks. When using random gossiping, communication with multiple peers in one gossiping round is allowed. The algorithms studied in this paper are considered under different network conditions, depending on the knowledge of the state of the neighboring nodes in the network. Different node behaviors, with respect to their degree of cooperation and compliance with the gossiping process, are also incorporated. From the exact analysis, several important performance metrics and design parameters are analytically determined. Based on the proposed metrics and parameters, the performance of the gossip-based dissemination or search schemes, as well as the impact of the design parameters, are evaluated.     

基于免疫算法的分层覆盖组播技术研究

为了克服传统的实时流媒体数据单播I、P组播等传输方式浪费网络带宽,甚至导致服务器过载的缺陷,提出了基于免疫算法的覆盖网络应用层组播树的构建方法。该方法以节点间网络延迟和节点的度作为约束条件,采用免疫算法划分组播岛、找出使整个系统"花费"最小的组播服务节点,实现了组播服务节点的全局最优选取。仿真结果表明,该方法有效可行,较采用传统的遗传算法具有更快的收敛速度和更高的搜索能力。     

Fast and proximity-aware multi-source overlay multicast under heterogeneous environment

Overlay multicast has been considered as one of the most important developments for the next generation Internet infrastructure. In this paper, we consider overlay multicast in the scenarios where any participant node is a potential data source. Existing multicast algorithms for single-source always require a long time to deliver messages or have high maintenance overhead when multiple data sources are allowed. There are other algorithms that are designed for multi-source scenarios. But they consume too much network resources and have a long convergence time because of proximity ignorance. To address the issues, we present FPCast, which leverages node heterogeneity and proximity information at the same time. Physically close nodes are grouped into clusters and each cluster selects a powerful, stable node as its rendezvous point. The rendezvous nodes form a DHT-based structure. Data messages are replicated and forwarded along implicit, source specific, and heterogeneity-aware multicast trees. We further reduce the delivery delay by introducing probabilistic forwarding scheme. We show the average delivery path length converges to O(logn) automatically (n is the number of nodes in the overlay). The simulation results demonstrate the superiority of our algorithm in terms of message delivery time and network resource consumption, in comparison with the previous randomized algorithms. The algorithm is also resilient to node failures.     

Multi-channel live streaming in service overlay network

Service overlay network (SON) provides an effective means to deploy quality of service (QoS)-guaranteed live streaming over today’s Internet. A major challenge in designing such a network is dealing with resource sharing among multiple channels. To achieve the best overall QoS in SON, we devise a new multi-channel live streaming scheme. First, we propose a multi-tree construction algorithm by infrastructure-based overlay multicast. The algorithm employs pre-allocated session degree constraints in overlay nodes to reserve resources for multiple channels, and constructs multiple trees by considering the total resource utilization of overlay nodes. Second, we propose a tree-aware queue scheduling algorithm to reduce the overlay processing delay in view of the entire overlay network. Scheduling priority is identified to trade off session priority with node location in different trees. From simulation and experimental results, the scheme achieves a differentiated control among different sessions, provides load balancing among overlay nodes, and improves the delay performance on SON.     

Approximate distributed top-<Emphasis Type="Italic">k</Emphasis> queries

We consider a distributed system where each node keeps a local count for items (similar to elections where nodes are ballot boxes and items are candidates). A top-k query in such a system asks which are the k items whose global count, across all nodes in the system, is the largest. In this paper, we present a Monte Carlo algorithm that outputs, with high probability, a set of k candidates which approximates the top-k items. The algorithm is motivated by sensor networks in that it focuses on reducing the individual communication complexity. In contrast to previous algorithms, the communication complexity depends only on the global scores and not on the partition of scores among nodes. If the number of nodes is large, our algorithm dramatically reduces the communication complexity when compared with deterministic algorithms. We show that the complexity of our algorithm is close to a lower bound on the cell-probe complexity of any non-interactive top-k approximation algorithm. We show that for some natural global distributions (such as the Geometric or Zipf distributions), our algorithm needs only polylogarithmic number of communication bits per node. An extended abstract of this paper appeared in Proc. 13th Int. Colloquium on Structural Information and Communication Complexity, SIROCCO 2006, Lecture Notes in Computer Science 4056, pp. 319–333.     

On the Convergence of Multicast Games in Directed Networks

We investigate the convergence of the price of anarchy after a limited number of moves in the classical multicast communication game when the underlying communication network is directed. Namely, a subset of nodes of the network are interested in receiving the transmission from a given source node and can share the cost of the used links according to fixed cost sharing methods. At each step, a single receiver is allowed to modify its communication strategy, that is to select a communication path from the source, and assuming a selfish or rational behavior, it will make a best response move, that is it will select a solution yielding the minimum possible payment or shared cost. We determine lower and upper bounds on the price of anarchy, that is the highest possible ratio among the overall cost of the links used by the receivers and the minimum possible cost realizing the required communications, after a limited number of moves under the fundamental Shapley cost sharing method. In particular, assuming that the initial set of connecting paths can be arbitrary, we show an $O(r\sqrt{r})We investigate the convergence of the price of anarchy after a limited number of moves in the classical multicast communication game when the underlying communication network is directed. Namely, a subset of nodes of the network are interested in receiving the transmission from a given source node and can share the cost of the used links according to fixed cost sharing methods. At each step, a single receiver is allowed to modify its communication strategy, that is to select a communication path from the source, and assuming a selfish or rational behavior, it will make a best response move, that is it will select a solution yielding the minimum possible payment or shared cost. We determine lower and upper bounds on the price of anarchy, that is the highest possible ratio among the overall cost of the links used by the receivers and the minimum possible cost realizing the required communications, after a limited number of moves under the fundamental Shapley cost sharing method. In particular, assuming that the initial set of connecting paths can be arbitrary, we show an O(r?r)O(r\sqrt{r}) upper bound on the price of anarchy after 2 rounds, during each of which all the receivers move exactly once, and a matching lower bound, that we also extend to W(r^k?{r})\Omega(r\sqrt[k]{r}) for any number k≥2 rounds, where r is the number of receivers. Similarly, exactly matching upper and lower bounds equal to r are determined for any number of rounds when starting from the empty state in which no path has been selected. Analogous results are obtained also with respect to other three natural cost sharing methods considered in the literature, that is the egalitarian, path-proportional and egalitarian-path proportional ones. Most results are also extended to the undirected case in which the communication links are bidirectional.     

Link scheduling in wireless sensor networks: Distributed edge-coloring revisited

We consider the problem of link scheduling in a sensor network employing a TDMA MAC protocol. Our algorithm consists of two phases. The first phase involves edge-coloring: an assignment of a color to each edge in the network such that no two edges incident on the same node are assigned the same color. Our main result for the first phase is a distributed edge-coloring algorithm that needs at most (Δ+1) colors, where Δ is the maximum degree of the network. To our knowledge, this is the first distributed algorithm that can edge-color a graph using at most (Δ+1) colors. The second phase uses the edge-coloring solution for link scheduling. We map each color to a unique timeslot and attempt to assign a direction of transmission along each edge such that the hidden terminal problem is avoided; an important result we obtain is a characterization of network topologies for which such an assignment exists. Next, we consider topologies for which a feasible transmission assignment does not exist for all edges, and obtain such an assignment using additional timeslots. Finally, we show that reversing the direction of transmission along every edge leads to another feasible direction of transmission. Using both the transmission assignments, we obtain a TDMA MAC schedule which enables two-way communication between every pair of adjacent sensor nodes. For acyclic topologies, we prove that at most 2(Δ+1) timeslots are required. Results for general topologies are demonstrated using simulations; for sparse graphs, we show that the number of timeslots required is around 2(Δ+1). We show that the message and time complexity of our algorithm is O(nΔ²+n²m), where n is the number of nodes and m is the number of edges in the network. Through simulations, we demonstrate that the energy consumption of our solution increases linearly with Δ. We also propose extensions to account for non-ideal radio characteristics.     

A hardware supported multicast scheme based on XY routing for 2-D mesh InfiniBand networks

The multicast operation is a useful operation in parallel applications. It is therefore important to ensure that for a given architecture, the parallel application runs efficiently. With the hardware-supported multicast of the InfiniBand Architecture (IBA), we propose a multicast scheme for m×n mesh InfiniBand networks based on XY routing. The basic concept of the proposed multicast scheme is to find the union sets of the output ports of switches, which are in the paths between the source node and each destination node in a multicast group. Furthermore, in the proposed scheme, we consider the usage of virtual lanes and evaluate their performance. We implement the proposed multicast scheme on a 2-D mesh InfiniBand network simulator. Several multicast configurations consisting of different message size, different traffic workload and different number of virtual lanes are simulated. The simulation results show that the proposed multicast scheme outperforms its corresponding unicast scheme for all simulation cases. The larger the message size, the larger the number of multicast source nodes, and the larger the size of the multicast group, the better the speedup that can be expected from the proposed multicast scheme. The usage of virtual lanes is also shown to improve the speed of the multicast operations.     

Strategies for interconnection networks: Some methods from graph theory

Interconnection networks require dense graphs in the sense that many nodes with relatively few links may be connected with relatively short paths. Some recent constructions of such dense graphs with a given maximal degree Δ and diameter D (known as (Δ, D) graphs) are reviewed here. The paper also contains an updated table of the best known (Δ, D) graphs.     

Location aware, dependable multicast for mobile ad hoc networks

This paper introduces dynamic source multicast (DSM), a new protocol for multi-hop wireless (i.e., ad hoc) networks for the multicast of a data packet from a source node to a group of mobile nodes in the network. The protocol assumes that, through the use of positioning system devices, each node knows its own geographic location and the current (global) time, and it is able to efficiently spread these measures to all other nodes. When a packet is to be multicast, the source node first locally computes a snapshot of the complete network topology from the collected node measures. A Steiner (i.e., multicast) tree for the addressed multicast group is then computed locally based on the snapshot, rather than maintained in a distributed manner. The resulting Steiner tree is then optimally encoded by using its unique Pr

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u" height="11" width="9">fer sequence and is included in the packet header as in, and extending the length of the header by no more than, the header of packets in source routing (unicast) techniques. We show that all the local computations are executed in polynomial time. More specifically, the time complexity of the local operation of finding a Steiner tree, and the encoding/decoding procedures of the related Prüfer sequence, is proven to be O(n²), where n is the number of nodes in the network. The protocol has been simulated in ad hoc networks with 30 and 60 nodes and with different multicast group sizes. We show that DSM delivers packets to all the nodes in a destination group in more than 90% of the cases. Furthermore, compared to flooding, DSM achieves improvements of up to 50% on multicast completion delay.     

Efficient Internet Multicast Routing Using Anycast Path Selection

A novel efficient and dynamic multicast routing protocol based on anycast routing techniques is presented. The contributions of the protocol differ from well-known shared-tree systems in two aspects: (1) Off-tree anycast routing: The nodes in the shared tree are formed into a virtual anycast group and multicast sources use anycast routing to select a better path from the source to one router in the group to achieve short delay and fault-tolerance. (2) On-tree dynamic routing: The shared-tree approach is extended with capability of alternative path selections. If a node becomes absent from the shared tree, some predefined backup path(s) is (are) used to bypass the node and enable dynamic multicast routing to continue. The protocol requires only the routers near the faulty node to be reconfigured, thus reducing the runtime overhead as compared with global reconfiguration. The simulation data demonstrates the efficiency of our routing protocol.     

A fast iterative-clique percolation method for identifying functional modules in protein interaction networks

Accumulating evidence suggests that biological systems are composed of interacting, separable, functional modules-groups of vertices within which connections are dense but between which they are sparse. Identifying these modules is likely through capturing the biologically meaningful interactions. In recent years, many algorithms have been developed for detecting such structures. These algorithms, however, are computationally demanding, which limits their applications. In this paper, we propose a fast iterative-clique percolation method (ICPM) for identifying overlapping functional modules in protein-protein interaction (PPI) networks. Our method is based on clique percolation method (CPM), and it not only considers the degree of nodes to minimize the search space (the vertices in k-cliques must have the degree of k − 1 at least), but also converts k-cliques to (k − 1)-cliques. It finds k-cliques by appending one node to (k − 1)-cliques. By testing our method on PPI networks, our analysis of the yeast PPI network suggests that most of these modules have well-supported biological significance.