19 research outputs found
The complexity of resolving conflicts on MAC
We consider the fundamental problem of multiple stations competing to
transmit on a multiple access channel (MAC). We are given stations out of
which at most are active and intend to transmit a message to other stations
using MAC. All stations are assumed to be synchronized according to a time
clock. If stations node transmit in the same round, then the MAC provides
the feedback whether , (collision occurred) or . When ,
then a single station is indeed able to successfully transmit a message, which
is received by all other nodes. For the above problem the active stations have
to schedule their transmissions so that they can singly, transmit their
messages on MAC, based only on the feedback received from the MAC in previous
round.
For the above problem it was shown in [Greenberg, Winograd, {\em A Lower
bound on the Time Needed in the Worst Case to Resolve Conflicts
Deterministically in Multiple Access Channels}, Journal of ACM 1985] that every
deterministic adaptive algorithm should take rounds
in the worst case. The fastest known deterministic adaptive algorithm requires
rounds. The gap between the upper and lower bound is
round. It is substantial for most values of : When constant and (for any constant , the lower bound is
respectively and O(n), which is trivial in both cases. Nevertheless,
the above lower bound is interesting indeed when poly(). In this
work, we present a novel counting argument to prove a tight lower bound of
rounds for all deterministic, adaptive algorithms, closing
this long standing open question.}Comment: Xerox internal report 27th July; 7 page
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 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 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
Achieving Dilution without Knowledge of Coordinates in the SINR Model
Considerable literature has been developed for various fundamental
distributed problems in the SINR (Signal-to-Interference-plus-Noise-Ratio)
model for radio transmission. A setting typically studied is when all nodes
transmit a signal of the same strength, and each device only has access to
knowledge about the total number of nodes in the network , the range from
which each node's label is taken , and the label of the device
itself. In addition, an assumption is made that each node also knows its
coordinates in the Euclidean plane. In this paper, we create a technique which
allows algorithm designers to remove that last assumption. The assumption about
the unavailability of the knowledge of the physical coordinates of the nodes
truly captures the `ad-hoc' nature of wireless networks.
Previous work in this area uses a flavor of a technique called dilution, in
which nodes transmit in a (predetermined) round-robin fashion, and are able to
reach all their neighbors. However, without knowing the physical coordinates,
it's not possible to know the coordinates of their containing (pivotal) grid
box and seemingly not possible to use dilution (to coordinate their
transmissions). We propose a new technique to achieve dilution without using
the knowledge of physical coordinates. This technique exploits the
understanding that the transmitting nodes lie in 2-D space, segmented by an
appropriate pivotal grid, without explicitly referring to the actual physical
coordinates of these nodes. Using this technique, it is possible for every weak
device to successfully transmit its message to all of its neighbors in
rounds, as long as the density of transmitting nodes in any
physical grid box is bounded by a known constant. This technique, we feel, is
an important generic tool for devising practical protocols when physical
coordinates of the nodes are not known.Comment: 10 page
Improved lower bound for deterministic broadcasting in radio networks
AbstractWe consider the problem of deterministic broadcasting in radio networks when the nodes have limited knowledge about the topology of the network. We show that for every deterministic broadcasting protocol there exists a network, of radius 2, for which the protocol takes at least Ω(n12) rounds for completing the broadcast. Our argument can be extended to prove a lower bound of Ω((nD)12) rounds for broadcasting in radio networks of radius D. This resolves one of the open problems posed in Kowalski and Pelc (2004) [24], where the authors proved a lower bound of Ω(n14) rounds for broadcasting in constant diameter networks.We prove the new lower bound for a special family of radius 2 networks. Each network of this family consists of O(n) components which are connected to each other via only the source node. At the heart of the proof is a novel simulation argument, which essentially says that any arbitrarily complicated strategy of the source node can be simulated by the nodes of the networks, if the source node just transmits partial topological knowledge about some component instead of arbitrary complicated messages. To the best of our knowledge this type of simulation argument is novel and may be useful in further improving the lower bound or may find use in other applications
Deterministic protocols in the SINR model without knowledge of coordinates
Much work has been developed for studying the classical broadcasting problem
in the SINR (Signal-to-Interference-plus-Noise-Ratio) model for wireless device
transmission. The setting typically studied is when all radio nodes transmit a
signal of the same strength. This work studies the challenging problem of
devising a distributed algorithm for multi-broadcasting, assuming a subset of
nodes are initially awake, for the SINR model when each device only has access
to knowledge about the total number of nodes in the network , the range from
which each node's label is taken , and the label of
the device itself. Specifically, we assume no knowledge of the physical
coordinates of devices and also no knowledge of the neighborhood of each node.
We present a deterministic protocol for this problem in
rounds. There is no known polynomial time deterministic algorithm in literature
for this setting, and it remains the principle open problem in this domain. A
lower bound of rounds is known for deterministic broadcasting
without local knowledge.
In addition to the above result, we present algorithms to achieve
multi-broadcast in rounds and create a backbone in
rounds, assuming that all nodes are initially awake. For a given backbone,
messages can be exchanged between every pair of connected nodes in the backbone
in rounds and between any node and its designated contact node in
the backbone in rounds.Comment: This is the author version of the paper which will appear in the
Journal of Computer and System Sciences. 36 pages, 1 table, 4 figures; v3
improves the presentation, style, and some technical matter of the pape