3,813 research outputs found
On the Classification of Universal Rotor-Routers
The combinatorial theory of rotor-routers has connections with problems of
statistical mechanics, graph theory, chaos theory, and computer science. A
rotor-router network defines a deterministic walk on a digraph G in which a
particle walks from a source vertex until it reaches one of several target
vertices. Motivated by recent results due to Giacaglia et al., we study
rotor-router networks in which all non-target vertices have the same type. A
rotor type r is universal if every hitting sequence can be achieved by a
homogeneous rotor-router network consisting entirely of rotors of type r. We
give a conjecture that completely classifies universal rotor types. Then, this
problem is simplified by a theorem we call the Reduction Theorem that allows us
to consider only two-state rotors. A rotor-router network called the
compressor, because it tends to shorten rotor periods, is introduced along with
an associated algorithm that determines the universality of almost all rotors.
New rotor classes, including boppy rotors, balanced rotors, and BURD rotors,
are defined to study this algorithm rigorously. Using the compressor the
universality of new rotor classes is proved, and empirical computer results are
presented to support our conclusions. Prior to these results, less than 100 of
the roughly 260,000 possible two-state rotor types of length up to 17 were
known to be universal, while the compressor algorithm proves the universality
of all but 272 of these rotor types
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
Network coding with periodic recomputation for minimum energy multicasting in mobile ad-hoc networks
We consider the problem of minimum-energy
multicast using network coding in mobile ad hoc networks
(MANETs). The optimal solution can be obtained by solving a
linear program every time slot, but it leads to high computational
complexity. In this paper, we consider a low-complexity
approach, network coding with periodic recomputation, which
recomputes an approximate solution at fixed time intervals, and
uses this solution during each time interval. As the network
topology changes slowly, we derive a theoretical bound on
the performance gap between our suboptimal solution and
the optimal solution. For complexity analysis, we assume that
interior-point method is used to solve a linear program at
the first time slot of each interval. Moreover, we can use the
suboptimal solution in the preceding interval as a good initial
solution of the linear program at each fixed interval. Based
on this interior-point method with a warm start strategy, we
obtain a bound on complexity. Finally, we consider an example
network scenario and minimize the complexity subject to the
condition that our solution achieves a given optimality gap
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