556 research outputs found
Prefix Codes: Equiprobable Words, Unequal Letter Costs
Describes a near-linear-time algorithm for a variant of Huffman coding, in
which the letters may have non-uniform lengths (as in Morse code), but with the
restriction that each word to be encoded has equal probability. [See also
``Huffman Coding with Unequal Letter Costs'' (2002).]Comment: proceedings version in ICALP (1994
The three-body problem and the Hannay angle
The Hannay angle has been previously studied for a celestial circular
restricted three-body system by means of an adiabatic approach. In the present
work, three main results are obtained. Firstly, a formal connection between
perturbation theory and the Hamiltonian adiabatic approach shows that both lead
to the Hannay angle; it is thus emphasised that this effect is already
contained in classical celestial mechanics, although not yet defined nor
evaluated separately. Secondly, a more general expression of the Hannay angle,
valid for an action-dependent potential is given; such a generalised expression
takes into account that the restricted three-body problem is a time-dependent,
two degrees of freedom problem even when restricted to the circular motion of
the test body. Consequently, (some of) the eccentricity terms cannot be
neglected {\it a priori}. Thirdly, we present a new numerical estimate for the
Earth adiabatically driven by Jupiter. We also point out errors in a previous
derivation of the Hannay angle for the circular restricted three-body problem,
with an action-independent potential.Comment: 11 pages. Accepted by Nonlinearit
Non-approximability and Polylogarithmic Approximations of the Single-Sink Unsplittable and Confluent Dynamic Flow Problems
Dynamic Flows were introduced by Ford and Fulkerson in 1958 to model flows over time. They define edge capacities to be the total amount of flow that can enter an edge in one time unit. Each edge also has a length, representing the time needed to traverse it. Dynamic Flows have been used to model many problems including traffic congestion, hop-routing of packets and evacuation protocols in buildings. While the basic problem of moving the maximal amount of supplies from sources to sinks is polynomial time solvable, natural minor modifications can make it NP-hard.
One such modification is that flows be confluent, i.e., all flows leaving a vertex must leave along the same edge. This corresponds to natural conditions in, e.g., evacuation planning and hop routing.
We investigate the single-sink Confluent Quickest Flow problem. The input is a graph with edge capacities and lengths, sources with supplies and a sink. The problem is to find a confluent flow minimizing the time required to send supplies to the sink. Our main results include:
a) Logarithmic Non-Approximability: Directed Confluent Quickest Flows cannot be approximated in polynomial time with an O(log n) approximation factor, unless P=NP.
b) Polylogarithmic Bicriteria Approximations: Polynomial time (O(log^8 n), O(log^2 kappa)) bicritera approximation algorithms for the Confluent Quickest Flow problem where kappa is the number of sinks, in both directed and undirected graphs.
Corresponding results are also developed for the Confluent Maximum Flow over time problem. The techniques developed also improve recent approximation algorithms for static confluent flows
^{59}Co NMR evidence for charge ordering below T_{CO}\sim 51 K in Na_{0.5}CoO_2
The CoO layers in sodium-cobaltates NaCoO may be viewed as
a spin triangular-lattice doped with charge carriers. The underlying
physics of the cobaltates is very similar to that of the high cuprates.
We will present unequivocal Co NMR evidence that below ,
the insulating ground state of the itinerant antiferromagnet
NaCoO () is induced by charge ordering.Comment: Phys. Rev. Lett. 100 (2008), in press. 4 figure
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