225 research outputs found
Friction under active control in systems with tailored degrees of freedom
Tribology subjects are deeply related to each other. Understanding them and their effect on the energy conversion process needs awareness about the highly non-equilibrium process happening at the atomic level. Sliding friction is generated at the interfaces. Understanding these interfacesâ properties is the most crucial part of modeling friction and, finally, finding the channels of losing energy, dissipation, or transformation to other forms of energy or other bodies. Sliding friction on âdry â solid surfaces at the nanoscale is the subject of this thesis. After reviewing some previous studies on dry friction, a two-dimensional bead-spring model will be set up for this work. Then, by employing molecular dynamics simulations, the energy dissipation through the internal degrees of freedom of the sliding object will be discussed. Also, the effect of structural defects and interaction anharmonicity on sliding friction will be investigated.2021-12-1
Distributed Dominating Set Approximations beyond Planar Graphs
The Minimum Dominating Set (MDS) problem is one of the most fundamental and
challenging problems in distributed computing. While it is well-known that
minimum dominating sets cannot be approximated locally on general graphs, over
the last years, there has been much progress on computing local approximations
on sparse graphs, and in particular planar graphs.
In this paper we study distributed and deterministic MDS approximation
algorithms for graph classes beyond planar graphs. In particular, we show that
existing approximation bounds for planar graphs can be lifted to bounded genus
graphs, and present (1) a local constant-time, constant-factor MDS
approximation algorithm and (2) a local -time
approximation scheme. Our main technical contribution is a new analysis of a
slightly modified variant of an existing algorithm by Lenzen et al.
Interestingly, unlike existing proofs for planar graphs, our analysis does not
rely on direct topological arguments.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0299
Walking Through Waypoints
We initiate the study of a fundamental combinatorial problem: Given a
capacitated graph , find a shortest walk ("route") from a source to a destination that includes all vertices specified by a set
: the \emph{waypoints}. This waypoint routing problem
finds immediate applications in the context of modern networked distributed
systems. Our main contribution is an exact polynomial-time algorithm for graphs
of bounded treewidth. We also show that if the number of waypoints is
logarithmically bounded, exact polynomial-time algorithms exist even for
general graphs. Our two algorithms provide an almost complete characterization
of what can be solved exactly in polynomial-time: we show that more general
problems (e.g., on grid graphs of maximum degree 3, with slightly more
waypoints) are computationally intractable
Vertex Disjoint Path in Upward Planar Graphs
The -vertex disjoint paths problem is one of the most studied problems in
algorithmic graph theory. In 1994, Schrijver proved that the problem can be
solved in polynomial time for every fixed when restricted to the class of
planar digraphs and it was a long standing open question whether it is
fixed-parameter tractable (with respect to parameter ) on this restricted
class. Only recently, \cite{CMPP}.\ achieved a major breakthrough and answered
the question positively. Despite the importance of this result (and the
brilliance of their proof), it is of rather theoretical importance. Their proof
technique is both technically extremely involved and also has at least double
exponential parameter dependence. Thus, it seems unrealistic that the algorithm
could actually be implemented. In this paper, therefore, we study a smaller
class of planar digraphs, the class of upward planar digraphs, a well studied
class of planar graphs which can be drawn in a plane such that all edges are
drawn upwards. We show that on the class of upward planar digraphs the problem
(i) remains NP-complete and (ii) the problem is fixed-parameter tractable.
While membership in FPT follows immediately from \cite{CMPP}'s general result,
our algorithm has only single exponential parameter dependency compared to the
double exponential parameter dependence for general planar digraphs.
Furthermore, our algorithm can easily be implemented, in contrast to the
algorithm in \cite{CMPP}.Comment: 14 page
Transiently Consistent SDN Updates: Being Greedy is Hard
The software-defined networking paradigm introduces interesting opportunities
to operate networks in a more flexible, optimized, yet formally verifiable
manner. Despite the logically centralized control, however, a Software-Defined
Network (SDN) is still a distributed system, with inherent delays between the
switches and the controller. Especially the problem of changing network
configurations in a consistent manner, also known as the consistent network
update problem, has received much attention over the last years. In particular,
it has been shown that there exists an inherent tradeoff between update
consistency and speed. This paper revisits the problem of updating an SDN in a
transiently consistent, loop-free manner. First, we rigorously prove that
computing a maximum (greedy) loop-free network update is generally NP-hard;
this result has implications for the classic maximum acyclic subgraph problem
(the dual feedback arc set problem) as well. Second, we show that for special
problem instances, fast and good approximation algorithms exist
- âŠ