LIPIcs

Fault-tolerant distributed algorithms play an important role in many critical/high-availability applications. These algorithms are notoriously difficult to implement correctly, due to asynchronous communication and the occurrence of faults, such as the network dropping messages or computers crashing. Nonetheless there is surprisingly little language and verification support to build distributed systems based on fault-tolerant algorithms. In this paper, we present some of the challenges that a designer has to overcome to implement a fault-tolerant distributed system. Then we review different models that have been proposed to reason about distributed algorithms and sketch how such a model can form the basis for a domain-specific programming language. Adopting a high-level programming model can simplify the programmer's life and make the code amenable to automated verification, while still compiling to efficiently executable code. We conclude by summarizing the current status of an ongoing language design and implementation project that is based on this idea

Population stability: regulating size in the presence of an adversary

We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size $N$. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and $\omega(\log^2 N)$ states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size

Improved Local Computation Algorithms for Constructing Spanners

A spanner of a graph is a subgraph that preserves lengths of shortest paths up to a multiplicative distortion. For every $k$, a spanner with size $O(n^{1+1/k})$ and stretch $(2k+1)$ can be constructed by a simple centralized greedy algorithm, and this is tight assuming Erd\H{o}s girth conjecture. In this paper we study the problem of constructing spanners in a local manner, specifically in the Local Computation Model proposed by Rubinfeld et al. (ICS 2011). We provide a randomized Local Computation Agorithm (LCA) for constructing $(2r-1)$-spanners with $\tilde{O}(n^{1+1/r})$ edges and probe complexity of $\tilde{O}(n^{1-1/r})$ for $r \in \{2,3\}$, where $n$ denotes the number of vertices in the input graph. Up to polylogarithmic factors, in both cases, the stretch factor is optimal (for the respective number of edges). In addition, our probe complexity for $r=2$, i.e., for constructing a $3$-spanner, is optimal up to polylogarithmic factors. Our result improves over the probe complexity of Parter et al. (ITCS 2019) that is $\tilde{O}(n^{1-1/2r})$ for $r \in \{2,3\}$. Both our algorithms and the algorithms of Parter et al. use a combination of neighbor-probes and pair-probes in the above-mentioned LCAs. For general $k\geq 1$, we provide an LCA for constructing $O(k^2)$-spanners with $\tilde{O}(n^{1+1/k})$ edges using $O(n^{2/3}\Delta^2)$ neighbor-probes, improving over the $\tilde{O}(n^{2/3}\Delta^4)$ algorithm of Parter et al. By developing a new randomized LCA for graph decomposition, we further improve the probe complexity of the latter task to be $O(n^{2/3-(1.5-\alpha)/k}\Delta^2)$, for any constant $\alpha>0$. This latter LCA may be of independent interest.Comment: RANDOM 202

Statistically Reliable and Secure Message Transmission in Directed Networks

Consider the following problem: a sender S and a receiver R are part of a directed synchronous network and connected through intermediate nodes. Specifically, there exists n node disjoint paths, also called as wires, which are directed from S to R and u wires, which are directed from R to S. Moreover, the wires from S to R are disjoint from the wires directed from R to S. There exists a centralized, static adversary who has unbounded computing power and who can control at most t wires between S and R in Byzantine fashion. S has a message m^S, which we wants to send to R. The challenge is to design a protocol, such that after interacting in phases as per the protocol, R should correctly output m^R = m^S, except with error probability 2^{-\Omega(\kappa)}, where \kappa is the error parameter. This problem is called as statistically reliable message transmission (SRMT). The problem of statistically secure message transmission (SSMT) has an additional requirement that at the end of the protocol, m^S should be information theoretically secure. Desmedt et.al have given the necessary and sufficient condition for the existence of SRMT and SSMT protocols in the above settings. They also presented an SSMT protocol, satisfying their characterization. Desmedt et.al claimed that their protocol is efficient and has polynomial computational and communication complexity. However, we show that it is not so. That is, we specify an adversary strategy, which may cause the protocol to have exponential computational and communication complexity. We then present new and efficient SRMT and SSMT protocols, satisfying the characterization of Desmedt et.al Finally we show that the our proposed protocols are communication optimal by deriving lower bound on the communication complexity of SRMT and SSMT protocols. As far our knowledge is concerned, our protocols are the first communication optimal SRMT and SSMT protocols in directed networks

Distributed Optimization of P2P Media Delivery Overlays

Media streaming over the Internet is becoming increasingly popular. Currently, most media is delivered using global content-delivery networks, providing a scalable and robust client-server model. However, content delivery infrastructures are expensive. One approach to reduce the cost of media delivery is to use peer-to-peer (P2P) overlay networks, where nodes share responsibility for delivering the media to one another. The main challenges in P2P media streaming using overlay networks include: (i) nodes should receive the stream with respect to certain timing constraints, (ii) the overlay should adapt to the changes in the network, e.g., varying bandwidth capacity and join/failure of nodes, (iii) nodes should be intentivized to contribute and share their resources, and (iv) nodes should be able to establish connectivity to the other nodes behind NATs. In this work, we meet these requirements by presenting P2P solutions for live media streaming, as well as proposing a distributed NAT traversal solution. First of all, we introduce a distributed market model to construct an approximately minimal height multiple-tree streaming overlay for content delivery, in gradienTv. In this system, we assume all the nodes are cooperative and execute the protocol. However, in reality, there may exist some opportunistic nodes, free-riders, that take advantage of the system, without contributing to content distribution. To overcome this problem, we extend our market model in Sepidar to be effective in deterring free-riders. However, gradienTv and Sepidar are tree-based solutions, which are fragile in high churn and failure scenarios. We present a solution to this problem in GLive that provides a more robust overlay by replacing the tree structure with a mesh. We show in simulation, that the mesh-based overlay outperforms the multiple-tree overlay. Moreover, we compare the performance of all our systems with the state-of-the-art NewCoolstreaming, and observe that they provide better playback continuity and lower playback latency than that of NewCoolstreaming under a variety of experimental scenarios. Although our distributed market model can be run against a random sample of nodes, we improve its convergence time by executing it against a sample of nodes taken from the Gradient overlay. The Gradient overlay organizes nodes in a topology using a local utility value at each node, such that nodes are ordered in descending utility values away from a core of the highest utility nodes. The evaluations show that the streaming overlays converge faster when our market model works on top of the Gradient overlay. We use a gossip-based peer sampling service in our streaming systems to provide each node with a small list of live nodes. However, in the Internet, where a high percentage of nodes are behind NATs, existing gossiping protocols break down. To solve this problem, we present Gozar, a NAT-friendly gossip-based peer sampling service that: (i) provides uniform random samples in the presence of NATs, and (ii) enables direct connectivity to sampled nodes using a fully distributed NAT traversal service. We compare Gozar with the state-of-the-art NAT-friendly gossip-based peer sampling service, Nylon, and show that only Gozar supports one-hop NAT traversal, and its overhead is roughly half of Nylon’s