A Dual Digraph Approach for Leaderless Atomic Broadcast (Extended Version)

Many distributed systems work on a common shared state; in such systems, distributed agreement is necessary for consistency. With an increasing number of servers, these systems become more susceptible to single-server failures, increasing the relevance of fault-tolerance. Atomic broadcast enables fault-tolerant distributed agreement, yet it is costly to solve. Most practical algorithms entail linear work per broadcast message. AllConcur -- a leaderless approach -- reduces the work, by connecting the servers via a sparse resilient overlay network; yet, this resiliency entails redundancy, limiting the reduction of work. In this paper, we propose AllConcur+, an atomic broadcast algorithm that lifts this limitation: During intervals with no failures, it achieves minimal work by using a redundancy-free overlay network. When failures do occur, it automatically recovers by switching to a resilient overlay network. In our performance evaluation of non-failure scenarios, AllConcur+ achieves comparable throughput to AllGather -- a non-fault-tolerant distributed agreement algorithm -- and outperforms AllConcur, LCR and Libpaxos both in terms of throughput and latency. Furthermore, our evaluation of failure scenarios shows that AllConcur+'s expected performance is robust with regard to occasional failures. Thus, for realistic use cases, leveraging redundancy-free distributed agreement during intervals with no failures improves performance significantly.Comment: Overview: 24 pages, 6 sections, 3 appendices, 8 figures, 3 tables. Modifications from previous version: extended the evaluation of AllConcur+ with a simulation of a multiple datacenters deploymen

On Approximating the Sum-Rate for Multiple-Unicasts

We study upper bounds on the sum-rate of multiple-unicasts. We approximate the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts network coding problem with $k$ independent sources. Our approximation algorithm runs in polynomial time and yields an upper bound on the joint source entropy rate, which is within an $O(\log^2 k)$ factor from the GNS cut. It further yields a vector-linear network code that achieves joint source entropy rate within an $O(\log^2 k)$ factor from the GNS cut, but \emph{not} with independent sources: the code induces a correlation pattern among the sources. Our second contribution is establishing a separation result for vector-linear network codes: for any given field $\mathbb{F}$ there exist networks for which the optimum sum-rate supported by vector-linear codes over $\mathbb{F}$ for independent sources can be multiplicatively separated by a factor of $k^{1-\delta}$, for any constant ${\delta>0}$, from the optimum joint entropy rate supported by a code that allows correlation between sources. Finally, we establish a similar separation result for the asymmetric optimum vector-linear sum-rates achieved over two distinct fields $\mathbb{F}_{p}$ and $\mathbb{F}_{q}$ for independent sources, revealing that the choice of field can heavily impact the performance of a linear network code.Comment: 10 pages; Shorter version appeared at ISIT (International Symposium on Information Theory) 2015; some typos correcte

Broadcasting in DMA-bound bounded degree graphs

AbstractBroadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. In [2], Bermond, Hell, Liestman and Peters studied the effect, on broadcasting capabilities, of placing an upper bound on the graph's degree. In this paper, we generalize their results allowing calls to involve more than two participants. We give lower bounds and construct bounded degree graphs which allow rapid broadcasting. Our constructions use the nation of compounding graphs in de Bruijin digraphs. We also obtain asymptotic upper and lower bounds for broadcast time, as the maximum degree increases

Achieving the Optimal Steaming Capacity and Delay Using Random Regular Digraphs in P2P Networks

In earlier work, we showed that it is possible to achieve $O(\log N)$ streaming delay with high probability in a peer-to-peer network, where each peer has as little as four neighbors, while achieving any arbitrary fraction of the maximum possible streaming rate. However, the constant in the $O(log N)$ delay term becomes rather large as we get closer to the maximum streaming rate. In this paper, we design an alternative pairing and chunk dissemination algorithm that allows us to transmit at the maximum streaming rate while ensuring that all, but a negligible fraction of the peers, receive the data stream with $O(\log N)$ delay with high probability. The result is established by examining the properties of graph formed by the union of two or more random 1-regular digraphs, i.e., directed graphs in which each node has an incoming and an outgoing node degree both equal to one

Power assignment problems in wireless communication

A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem. This paper considers several problems of that kind; for example one problem studied before in (Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) and (Helmut Alt et al.: Minimum-cost coverage of point sets by disks, SCG 2006) aims to select and assign powers to $k$ of the stations such that all other stations are within reach of at least one of the selected stations. We improve the running time for obtaining a $(1+\epsilon)$-approximate solution for this problem from $n^{((\alpha/\epsilon)^{O(d)})}$ as reported by Bil{\`o} et al. (see Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) to $O\left( n+ {\left(\frac{k^{2d+1}}{\epsilon^d}\right)}^{ \min{\{\; 2k,\;\; (\alpha/\epsilon)^{O(d)} \;\}} } \right)$ that is, we obtain a running time that is \emph{linear} in the network size. Further results include a constant approximation algorithm for the TSP problem under squared (non-metric!) edge costs, which can be employed to implement a novel data aggregation protocol, as well as efficient schemes to perform $k$-hop multicasts

Topological Interference Management With Decoded Message Passing

The topological interference management (TIM) problem studies partially-connected interference networks with no channel state information except for the network topology (i.e., connectivity graph) at the transmitters. In this paper, we consider a similar problem in the uplink cellular networks, while message passing is enabled at the receivers (e.g., base stations), so that the decoded messages can be routed to other receivers via backhaul links to help further improve network performance. For this TIM problem with decoded message passing (TIM-MP), we model the interference pattern by conflict digraphs, connect orthogonal access to the acyclic set coloring on conflict digraphs, and show that one-to-one interference alignment boils down to orthogonal access because of message passing. With the aid of polyhedral combinatorics, we identify the structural properties of certain classes of network topologies where orthogonal access achieves the optimal degrees-of-freedom (DoF) region in the information-theoretic sense. The relation to the conventional index coding with simultaneous decoding is also investigated by formulating a generalized index coding problem with successive decoding as a result of decoded message passing. The properties of reducibility and criticality are also studied, by which we are able to prove the linear optimality of orthogonal access in terms of symmetric DoF for the networks up to four users with all possible network topologies (218 instances). Practical issues of the tradeoff between the overhead of message passing and the achievable symmetric DoF are also discussed, in the hope of facilitating efficient backhaul utilization

k-Set Agreement in Communication Networks with Omission Faults

We consider an arbitrary communication network G where at most f messages can be lost at each round, and consider the classical k-set agreement problem in this setting. We characterize exactly for which f the k-set agreement problem can be solved on G. The case with k = 1, that is the Consensus problem, has first been introduced by Santoro and Widmayer in 1989, the characterization is already known from [Coulouma/Godard/Peters, TCS, 2015]. As a first contribution, we present a detailed and complete characterization for the 2-set problem. The proof of the impossibility result uses topological methods. We introduce a new subdivision approach for these topological methods that is of independent interest. In the second part, we show how to extend to the general case with k in N. This characterization is the first complete characterization for this kind of synchronous message passing model, a model that is a subclass of the family of oblivious message adversaries

Lower bounds on systolic gossip

AbstractGossiping is an extensively investigated information dissemination process in which each processor has a distinct item of information and has to collect all the items possessed by the other processors. In this paper we provide an innovative and general lower bound technique relying on the novel notion of delay digraph of a gossiping protocol and on the use of matrix norm methods. Such a technique is very powerful and allows the determination of new and significantly improved lower bounds in many cases. In fact, we derive the first general lower bound on the gossiping time of systolic protocols, i.e., constituted by a periodic repetition of simple communication steps. In particular, given any network of n processors and any systolic period s, in the directed and the undirected half-duplex cases every s-systolic gossip protocol takes at least log(n)/log(1/λ)−O(loglog(n)) time steps, where λ is the unique solution between 0 and 1 of λ·p⌊s/2⌋(λ)·p⌈s/2⌉(λ)=1, with pi(λ)=1+λ2+⋯+λ2i−2 for any integer i>0. We then provide improved lower bounds in the directed and half-duplex cases for many well-known network topologies, such as Butterfly, de Bruijn, and Kautz graphs. All the results are extended also to the full-duplex case. Our technique is very general, as for s→∞ it allows the determination of improved results even for non-systolic protocols. In fact, for general networks, as a simple corollary it yields a lower bound only an O(loglog(n)) additive factor far from the general one independently proved in [Proc. 1st ACM Symposium on Parallel Algorithms and Architectures (SPAA), 1989, p. 318; Topics in Combinatorics and Graph Theory (1990) 451; SIAM Journal on Computing 21(1) (1992) 111; Discrete Applied Mathematics 42 (1993) 75] for all graphs and any (non-systolic) gossip protocol. Moreover, for specific networks, it significantly improves with respect to the previously known results, even in the full-duplex case. Correspondingly, better lower bounds on the gossiping time of non-systolic protocols are determined in the directed, half-duplex and full-duplex cases for Butterfly, de Bruijn, and Kautz graphs. Even if in this paper we give only a limited number of examples, our technique has wide applicability and gives a general framework that often allows to get improved lower bounds on the gossiping time of systolic and non-systolic protocols in the directed, half-duplex and full-duplex cases