3,422 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
Connected and internal graph searching
This paper is concerned with the graph searching game. The search number es(G) of a graph G is the smallest number of searchers required to clear G. A search strategy is monotone (m) if no recontamination ever occurs. It is connected (c) if the set of clear edges always forms a connected subgraph. It is internal (i) if the removal of searchers is not allowed. The difficulty of the connected version and of the monotone internal version of the graph searching problem comes from the fact that, as shown in the paper, none of these problems is minor closed for arbitrary graphs, as opposed to all known variants of the graph searching problem. Motivated by the fact that connected graph searching, and monotone internal graph searching are both minor closed in trees, we provide a complete characterization of the set of trees that can be cleared by a given number of searchers. In fact, we show that, in trees, there is only one obstruction for monotone internal search, as well as for connected search, and this obstruction is the same for the two problems. This allows us to prove that, for any tree T, mis(T)= cs(T). For arbitrary graphs, we prove that there is a unique chain of inequalities linking all the search numbers above. More precisely, for any graph G, es(G)= is(G)= ms(G)leq mis(G)leq cs(G)= ics(G)leq mcs(G)=mics(G). The first two inequalities can be strict. In the case of trees, we have mics(G)leq 2 es(T)-2, that is there are exactly 2 different search numbers in trees, and these search numbers differ by a factor of 2 at most.Postprint (published version
AFM Dissipation Topography of Soliton Superstructures in Adsorbed Overlayers
In the atomic force microscope, the nanoscale force topography of even
complex surface superstructures is extracted by the changing vibration
frequency of a scanning tip. An alternative dissipation topography with similar
or even better contrast has been demonstrated recently by mapping the
(x,y)-dependent tip damping but the detailed damping mechanism is still
unknown. Here we identify two different tip dissipation mechanisms: local
mechanical softness and hysteresis. Motivated by recent data, we describe both
of them in a onedimensional model of Moire' superstructures of incommensurate
overlayers. Local softness at "soliton" defects yields a dissipation contrast
that can be much larger than the corresponding density or corrugation contrast.
At realistically low vibration frequencies, however, a much stronger and more
effective dissipation is caused by the tip-induced nonlinear jumping of the
soliton, naturally developing bistability and hysteresis. Signatures of this
mechanism are proposed for experimental identification.Comment: 5 pages, 5 figures, Phys Rev B 81, 045417 (2010
Line-Recovery by Programmable Particles
Shape formation has been recently studied in distributed systems of
programmable particles. In this paper we consider the shape recovery problem of
restoring the shape when of the particles have crashed. We focus on the
basic line shape, used as a tool for the construction of more complex
configurations.
We present a solution to the line recovery problem by the non-faulty
anonymous particles; the solution works regardless of the initial distribution
and number of faults, of the local orientations of the non-faulty
entities, and of the number of non-faulty entities activated in each round
(i.e., semi-synchronous adversarial scheduler)
Solitons and exact velocity quantization of incommensurate sliders
We analyze in some detail the recently discovered velocity quantization
phenomena in the classical motion of an idealized one-dimensional solid
lubricant, consisting of a harmonic chain interposed between two periodic
sliders. The ratio w = v_cm/v_ext of the chain center-of-mass velocity to the
externally imposed relative velocity of the sliders is pinned to exact
``plateau'' values for wide ranges of parameters, such as sliders corrugation
amplitudes, external velocity, chain stiffness and dissipation, and is strictly
determined by the commensurability ratios alone. The phenomenon is caused by
one slider rigidly dragging the density solitons (kinks/antikinks) that the
chain forms with the other slider. Possible consequences of these results for
some real systems are discussed.Comment: 12 pages 6 figures. Small fixup after Referee's comments. In print in
J. Phys.: Condens. Matte
Hysteresis from dynamically pinned sliding states
We report a surprising hysteretic behavior in the dynamics of a simple
one-dimensional nonlinear model inspired by the tribological problem of two
sliding surfaces with a thin solid lubricant layer in between. In particular,
we consider the frictional dynamics of a harmonic chain confined between two
rigid incommensurate substrates which slide with a fixed relative velocity.
This system was previously found, by explicit solution of the equations of
motion, to possess plateaus in parameter space exhibiting a remarkable
quantization of the chain center-of-mass velocity (dynamic pinning) solely
determined by the interface incommensurability. Starting now from this
quantized sliding state, in the underdamped regime of motion and in analogy to
what ordinarily happens for static friction, the dynamics exhibits a large
hysteresis under the action of an additional external driving force F_ext. A
critical threshold value F_c of the adiabatically applied force F_ext is
required in order to alter the robust dynamics of the plateau attractor. When
the applied force is decreased and removed, the system can jump to intermediate
sliding regimes (a sort of ``dynamic'' stick-slip motion) and eventually
returns to the quantized sliding state at a much lower value of F_ext. On the
contrary no hysteretic behavior is observed as a function of the external
driving velocity.Comment: 12 pages, 5 figures, ECOSS 200
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