Bogdan S. Chlebus

Deterministic broadcasting in ad hoc radio networks

Abstract. 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

Deterministic Radio Broadcasting

O(n^{11/6})

Domino-tiling games

. 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.

Adversarial queuing on the multiple-access channel

We consider broadcasting in radio networks: one node of the network knows a message that needs to be learned by all the remaining nodes. We seek distributed deterministic algorithms to perform this task. Radio networks are modeled as directed graphs. They are unknown, in the sense that nodes are not assumed to know their neighbors, nor the size of the network, they are aware only of their individual identifying numbers. If more than one message is delivered to a node in a step then the node cannot hear any of them. Nodes cannot distinguish between such collisions and the case when no messages have been delivered in a step. The fastest previously known deterministic algorithm for deterministic distributed broadcasting in unknown radio networks was presented in [6], it worked in time O(n11/6). We develop three new deterministic distributed algorithms. Algorithm A develops further the ideas of [6] and operates in time O(n1:77291) = O(n9/5), for general networks, and in time O(n1+a+H(a)+o(1)) for sparse networks with in-degrees O(na) fora < 1=2; here H is the entropy function. Algorithm B uses a new approach and works in time O(n3/2 log1/2 n) for general networks or O(n1+a+o(1)) for sparse networks. Algorithm C further improves the performance for general networks running in time O(n3/2).

Oblivious gossiping in ad-hoc radio networks

Abstract Games in which players build domino tilings are considered. The computational complexity of problems of existence of winning strategies is investigated. These problems are shown to be complete in the respective complexity classes, e.g., SQUARE TILING GAME is complete in PSPACE, HIGH TILING GAME is complete in 2EXPTIME and has a doubly exponential time lower bound. As an application, new simple hardness proofs for certain propositional logics are obtained.

Performing tasks on synchronous restartable message-passing processors

We consider broadcasting on the multiple-access channel when packets are injected continuously. Multiple-access channel is a synchronous system with the properties that a single transmission at a round delivers the message to all nodes, while multiple simultaneous transmissions result in a conflict which prevents delivering messages to any among the recipients. The traditional approach to dynamic broadcasting has been concerned with stability of protocols under suitable stochastic assumptions about injection rates. We study deterministic protocols competing against adversaries restricted by injection rate and burstiness of traffic. Stability means that the number of packets in queues is bounded by a constant in any execution, for a given number of stations, protocol, and adversary. Strong stability denotes the property that the number of queued packets is proportional to the burstiness of traffic, that is, the maximum number of packets an adversary may inject simultaneously. There are three natural classes of protocols we consider. The weakest acknowledgement-based protocols have a station rely on its local clock and on a feedback from the channel during its own attempts of transmissions. Full-sensing protocols allow a station to rely on a global clock and to store the history of all the previous successes/failures of transmissions in the course of an execution. A station running an adaptive protocol can rely on a global clock, may add control bits to be piggybacked on messages, and may store the complete history of the feedback from the channel during an execution. It turns out that there is no adaptive broadcast protocol stable for the injection rate λ = 1 for the multiple-access channel with at least n ≥ 4 stations, even when collision detection is available. We show that a simple full-sensing protocol is universally stable, which means it can handle any constant injection rate λ ‹ 1 in a stable manner. A more involved full-sensing protocol is shown to be both universally stable and strongly-stable for injection rate ρ (n) ≤ 1over>d lg2 n, where d>0 is a sufficiently large constant and n is the number of stations. We show that there is an acknowledgement-based protocol that is strongly stable for injection rate ρ(n)≤ 1<over>d lg2 n, for a sufficiently large constant d0. Regarding the stability of acknowledgement-based protocols, we show that no such a protocol is stable for injection rate ρ(n)> 2<over>1+lg n. This implies that there are no universally stable acknowledgement-based protocols. We show that when collision detection is available, then a simple full-sensing protocol is both universally stable and strongly stable for injection rate ρ(n)≤ 1<over>2 lgn. As a complementary fact, we prove that no adaptive protocol for a channel with collision detection can be strongly stable for the injection rate that satisfies ρ (n) = ω (1<over>log n). This shows that the protocol we give is optimal with respect to injection rates it handles in a strongly stable manner.

On the wake-up problem in radio networks

We study oblivious deterministic and randomized algorithms for gossiping in unknown radio networks. In oblivious algorithms the fact (or probability in case of randomized algorithm) that a processor transmits or not at a given time-step depends solely on its identification number, the total number of processors and the number of the time-step. We distinguish oblivious deterministic algorithms which allow only one processor to transmit in each time-step and term them singleton algorithms. We also distinguish oblivious randomized algorithms where in each time-step all processors have equal probability of transmission, and call them uniform. The merit of oblivious algorithms, especially the singleton and uniform ones, is that they are simple and easy to implement. We observe that gossiping in unknown radio networks on <i>n</i> nodes can be completed in time (<i>n</i> - 1)(<i>n</i> - 2) + 4 by a singleton algorithm. On the other hand, we show that any singleton algorithm takes at least <i>n</i>² - <i>&Ogr;</i>(<i>n</i>^7/4+∈) steps, for any ∈ > 0, whereas any deterministic oblivious algorithm requires at least <i>n</i>²/2 - <i>&Ogr;</i>(<i>n</i>) steps to complete the gossiping. We prove also that there is an oblivious deterministic algorithm for gossiping working in time <i>n</i>² - <i>w</i>(<i>n</i>). Next we show that a uniform oblivious randomized algorithm completes gossiping with high probability in time <i>&Ogr;</i>(min{<i>m, Dd</i>} log² <i>n</i>), where <i>m</i> denotes the number of edges, <i>D</i> is the eccentricity and <i>d</i> the maximum, in-degree in the network. Note that this upper bound is poly-logarithmic in <i>n</i> if <i>D, d</i> = <i>&Ogr;</i>(<i>poly</i> log <i>n</i>). The best related deterministic gossiping algorithm, in terms of performance expressed with respect to <i>n</i>, <i>D</i>, <i>d</i>, has been previously given by Clementi et al. [13], it works in time <i>&Ogr;</i>(<i>Dd</i>² log³ <i>n</i>). We prove also that the upper bound attained by our uniform oblivious randomized algorithm is asymptotically optimal (up to a log-square factor) for a wide range of parameters <i>m</i>, <i>D</i> and <i>d</i> in the class of uniform oblivious randomized algorithms. Finally we observe that in case of symmetric networks the aforementioned oblivious randomized algorithm completes gossiping with high probability in time <i>&Ogr;</i>(<i>n</i> log² <i>n</i>) and that a known deterministic constructive broadcasting algorithm can be adopted to perform oblivious gossiping in time <i>&Ogr;</i>(<i>n</i>^3/2).

On Finding Optimal Discretizations for Two Attributes

Summary. This work considers the problem of performing t tasks in a distributed system of p fault-prone processors. This problem, called do-all herein, was introduced by Dwork, Halpern and Waarts. The solutions presented here are for the model of computation that abstracts a synchronous message-passing distributed system with processor stop-failures and restarts. We present two new algorithms based on a new aggressive coordination paradigm by which multiple coordinators may be active as the result of failures. The first algorithm is tolerant of

Almost optimal explicit selectors

f < p

Adversarial Queuing on the Multiple Access Channel

stop-failures and does not allow restarts. Its available processor steps (work) complexity is