Distributed Algorithms in Synchronous Broadcasting Networks

In this paper we consider a synchronous broadcasting network, a distributed computation model which represents communication networks that are used extensively in practice. This is the first work we know of that deals with this model in a theoretical context. The problem we consider is a basic problem of information sharing, the computation of the multiple identification function. That is, given a network of p processors, each of which contains an n-bit string of information, the question is how every processor can compute the subset of processors which have the same information as itself. The problem was suggested by Yao in his classical paper in communication complexity [17], as a generalization of the two-processor case studied in that paper. The immediate algorithm which solves this problem takes O(np) time (time = communication time in bits, which is our complexity measure). We present the following algorithms: - a. An algorithm which takes advantage of properties of strings, uses a very simple scheduling policy, and does not use arithmetic operations. (In fact, the processor can be a Turing machine). 'the algorithm's complexity is O(nlog2p+p). - b. An algorithm which uses a simulation of sorting networks by the distributed system. If t(p) is the depth of the sorting network of p processors, then our algorithm takes O( n t(p) + p) time. Using recent results on sorting networks we get an O(nlogp+p) (impractical) algorithm. The algorithm also uses addition and subtraction operations. -c. By letting the processor use modular arithmetic operations as well, we can use Yao's probabilistic version, modify our algorithms and get probabilistic algorithms (with small error) where logn replaces n in the complexity expressions. To prove lower bounds for the problem we use Yao's result to get an fl(n) bound, and we also show an fl(p) bound. We suggest open problems concerning new techniques for proving lower bounds in the presence of broadcasting, as well as other problems about efficient use of the model and comparisons between different models of distributed computation

Distributed Algorithms in Synchronous Broadcasting Networks

In this paper we consider a synchronous broadcasting network, a distributed computation model which represents communication networks that are used extensively in practice. This is the first work we know of that deals with this model in a theoretical context. The problem we consider is a basic problem of information sharing, the computation of the multiple identification function. That is, given a network of p processors, each of which contains an n-bit string of information, the question is how every processor can compute the subset of processors which have the same information as itself. The problem was suggested by Yao in his classical paper in communication complexity [17], as a generalization of the two-processor case studied in that paper. The immediate algorithm which solves this problem takes O(np) time (time = communication time in bits, which is our complexity measure). We present the following algorithms: - a. An algorithm which takes advantage of properties of strings, uses a very simple scheduling policy, and does not use arithmetic operations. (In fact, the processor can be a Turing machine). 'the algorithm's complexity is O(nlog2p+p). - b. An algorithm which uses a simulation of sorting networks by the distributed system. If t(p) is the depth of the sorting network of p processors, then our algorithm takes O( n t(p) + p) time. Using recent results on sorting networks we get an O(nlogp+p) (impractical) algorithm. The algorithm also uses addition and subtraction operations. -c. By letting the processor use modular arithmetic operations as well, we can use Yao's probabilistic version, modify our algorithms and get probabilistic algorithms (with small error) where logn replaces n in the complexity expressions. To prove lower bounds for the problem we use Yao's result to get an fl(n) bound, and we also show an fl(p) bound. We suggest open problems concerning new techniques for proving lower bounds in the presence of broadcasting, as well as other problems about efficient use of the model and comparisons between different models of distributed computation

Faster Gossiping in Bidirectional Radio Networks with Large Labels

We consider unknown ad-hoc radio networks, when the underlying network is bidirectional and nodes can have polynomially large labels. For this model, we present a deterministic protocol for gossiping which takes $O(n \lg^2 n \lg \lg n)$ rounds. This improves upon the previous best result for deterministic gossiping for this model by [Gasienec, Potapov, Pagourtizis, Deterministic Gossiping in Radio Networks with Large labels, ESA (2002)], who present a protocol of round complexity $O(n \lg^3 n \lg \lg n)$ for this problem. This resolves open problem posed in [Gasienec, Efficient gossiping in radio networks, SIROCCO (2009)], who cite bridging gap between lower and upper bounds for this problem as an important objective. We emphasize that a salient feature of our protocol is its simplicity, especially with respect to the previous best known protocol for this problem

Optimal Collision/Conflict-free Distance-2 Coloring in Synchronous Broadcast/Receive Tree Networks

This article is on message-passing systems where communication is (a) synchronous and (b) based on the "broadcast/receive" pair of communication operations. "Synchronous" means that time is discrete and appears as a sequence of time slots (or rounds) such that each message is received in the very same round in which it is sent. "Broadcast/receive" means that during a round a process can either broadcast a message to its neighbors or receive a message from one of them. In such a communication model, no two neighbors of the same process, nor a process and any of its neighbors, must be allowed to broadcast during the same time slot (thereby preventing message collisions in the first case, and message conflicts in the second case). From a graph theory point of view, the allocation of slots to processes is know as the distance-2 coloring problem: a color must be associated with each process (defining the time slots in which it will be allowed to broadcast) in such a way that any two processes at distance at most 2 obtain different colors, while the total number of colors is "as small as possible". The paper presents a parallel message-passing distance-2 coloring algorithm suited to trees, whose roots are dynamically defined. This algorithm, which is itself collision-free and conflict-free, uses $\Delta + 1$ colors where $\Delta$ is the maximal degree of the graph (hence the algorithm is color-optimal). It does not require all processes to have different initial identities, and its time complexity is $O(d \Delta)$, where d is the depth of the tree. As far as we know, this is the first distributed distance-2 coloring algorithm designed for the broadcast/receive round-based communication model, which owns all the previous properties.Comment: 19 pages including one appendix. One Figur

Data Dissemination in Unified Dynamic Wireless Networks

We give efficient algorithms for the fundamental problems of Broadcast and Local Broadcast in dynamic wireless networks. We propose a general model of communication which captures and includes both fading models (like SINR) and graph-based models (such as quasi unit disc graphs, bounded-independence graphs, and protocol model). The only requirement is that the nodes can be embedded in a bounded growth quasi-metric, which is the weakest condition known to ensure distributed operability. Both the nodes and the links of the network are dynamic: nodes can come and go, while the signal strength on links can go up or down. The results improve some of the known bounds even in the static setting, including an optimal algorithm for local broadcasting in the SINR model, which is additionally uniform (independent of network size). An essential component is a procedure for balancing contention, which has potentially wide applicability. The results illustrate the importance of carrier sensing, a stock feature of wireless nodes today, which we encapsulate in primitives to better explore its uses and usefulness.Comment: 28 pages, 2 figure