1,573 research outputs found
Shortest, Fastest, and Foremost Broadcast in Dynamic Networks
Highly dynamic networks rarely offer end-to-end connectivity at a given time.
Yet, connectivity in these networks can be established over time and space,
based on temporal analogues of multi-hop paths (also called {\em journeys}).
Attempting to optimize the selection of the journeys in these networks
naturally leads to the study of three cases: shortest (minimum hop), fastest
(minimum duration), and foremost (earliest arrival) journeys. Efficient
centralized algorithms exists to compute all cases, when the full knowledge of
the network evolution is given.
In this paper, we study the {\em distributed} counterparts of these problems,
i.e. shortest, fastest, and foremost broadcast with termination detection
(TDB), with minimal knowledge on the topology.
We show that the feasibility of each of these problems requires distinct
features on the evolution, through identifying three classes of dynamic graphs
wherein the problems become gradually feasible: graphs in which the
re-appearance of edges is {\em recurrent} (class R), {\em bounded-recurrent}
(B), or {\em periodic} (P), together with specific knowledge that are
respectively (the number of nodes), (a bound on the recurrence
time), and (the period). In these classes it is not required that all pairs
of nodes get in contact -- only that the overall {\em footprint} of the graph
is connected over time.
Our results, together with the strict inclusion between , , and ,
implies a feasibility order among the three variants of the problem, i.e.
TDB[foremost] requires weaker assumptions on the topology dynamics than
TDB[shortest], which itself requires less than TDB[fastest]. Reversely, these
differences in feasibility imply that the computational powers of ,
, and also form a strict hierarchy
Shortest, Fastest, and Foremost Broadcast in Dynamic Networks *
Highly dynamic networks rarely offer end-to-end connectivity at a given time. Connectivity in these networks can be established over time and space, based on temporal analogues of multi-hop paths (also called journeys). In a seminal work, Our results, together with the strict inclusion between P, B, and R, implies a feasibility order among the three variants of the problem, i.e. TDB[f oremost] requires weaker assumptions on the topology dynamics than TDB [shortest], which itself requires less than TDB[f astest]. Reversely, these differences in feasibility imply that the computational powers of Rn, B ∆ , and Pp also form a strict hierarchy
Time-Varying Graphs and Dynamic Networks
The past few years have seen intensive research efforts carried out in some
apparently unrelated areas of dynamic systems -- delay-tolerant networks,
opportunistic-mobility networks, social networks -- obtaining closely related
insights. Indeed, the concepts discovered in these investigations can be viewed
as parts of the same conceptual universe; and the formal models proposed so far
to express some specific concepts are components of a larger formal description
of this universe. The main contribution of this paper is to integrate the vast
collection of concepts, formalisms, and results found in the literature into a
unified framework, which we call TVG (for time-varying graphs). Using this
framework, it is possible to express directly in the same formalism not only
the concepts common to all those different areas, but also those specific to
each. Based on this definitional work, employing both existing results and
original observations, we present a hierarchical classification of TVGs; each
class corresponds to a significant property examined in the distributed
computing literature. We then examine how TVGs can be used to study the
evolution of network properties, and propose different techniques, depending on
whether the indicators for these properties are a-temporal (as in the majority
of existing studies) or temporal. Finally, we briefly discuss the introduction
of randomness in TVGs.Comment: A short version appeared in ADHOC-NOW'11. This version is to be
published in Internation Journal of Parallel, Emergent and Distributed
System
DMVP: Foremost Waypoint Coverage of Time-Varying Graphs
We consider the Dynamic Map Visitation Problem (DMVP), in which a team of
agents must visit a collection of critical locations as quickly as possible, in
an environment that may change rapidly and unpredictably during the agents'
navigation. We apply recent formulations of time-varying graphs (TVGs) to DMVP,
shedding new light on the computational hierarchy of TVG classes by analyzing them in the
context of graph navigation. We provide hardness results for all three classes,
and for several restricted topologies, we show a separation between the classes
by showing severe inapproximability in , limited approximability
in , and tractability in . We also give topologies in
which DMVP in is fixed parameter tractable, which may serve as a
first step toward fully characterizing the features that make DMVP difficult.Comment: 24 pages. Full version of paper from Proceedings of WG 2014, LNCS,
Springer-Verla
The Next 700 Impossibility Results in Time-Varying Graphs
We address highly dynamic distributed systems modeled by time-varying graphs
(TVGs). We interest in proof of impossibility results that often use informal
arguments about convergence. First, we provide a distance among TVGs to define
correctly the convergence of TVG sequences. Next, we provide a general
framework that formally proves the convergence of the sequence of executions of
any deterministic algorithm over TVGs of any convergent sequence of TVGs.
Finally, we illustrate the relevance of the above result by proving that no
deterministic algorithm exists to compute the underlying graph of any
connected-over-time TVG, i.e., any TVG of the weakest class of long-lived TVGs
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