386 research outputs found
Sign of the crossed conductances at a FSF double interface
Crossed conductance in hybrid Ferromagnet / Superconductor / Ferromagnet
(FSF) structures results from the competition between normal transmission and
Andreev reflection channels. Crossed Andreev reflection (CAR) and elastic
cotunneling (EC) between the ferromagnets are dressed by local Andreev
reflections, which play an important role for transparent enough interfaces and
intermediate spin polarizations. This modifies the simple result previously
obtained at lowest order, and can explain the sign of the crossed resistances
in a recent experiment [D. Beckmann {\sl et al.}, cond-mat/0404360]. This holds
both in the multiterminal hybrid structure model (where phase averaging over
the Fermi oscillations is introduced ``by hand'' within the approximation of a
single non local process) and for infinite planar interfaces (where phase
averaging naturally results in the microscopic solution with multiple non local
processes).Comment: 9 pages, 7 figure
Point Set Isolation Using Unit Disks is NP-complete
We consider the situation where one is given a set S of points in the plane
and a collection D of unit disks embedded in the plane. We show that finding a
minimum cardinality subset of D such that any path between any two points in S
is intersected by at least one disk is NP-complete. This settles an open
problem raised by Matt Gibson et al[1]. Using a similar reduction, we show that
finding a minimum cardinality subset D' of D such that R^2 - (D - D') consists
of a single connected region is also NP-complete. Lastly, we show that the
Multiterminal Cut Problem remains NP-complete when restricted to unit disk
graphs
Minimum Separation for Single-Layer Channel Routing
We present a linear-time algorithm for determining the minimum height of a single-layer routing channel. The algorithm handles single-sided connections and multiterminal nets. It yields a simple routability test for single-layer switchboxes, correcting an error in the literature
Optimal Embedding of Functions for In-Network Computation: Complexity Analysis and Algorithms
We consider optimal distributed computation of a given function of
distributed data. The input (data) nodes and the sink node that receives the
function form a connected network that is described by an undirected weighted
network graph. The algorithm to compute the given function is described by a
weighted directed acyclic graph and is called the computation graph. An
embedding defines the computation communication sequence that obtains the
function at the sink. Two kinds of optimal embeddings are sought, the embedding
that---(1)~minimizes delay in obtaining function at sink, and (2)~minimizes
cost of one instance of computation of function. This abstraction is motivated
by three applications---in-network computation over sensor networks, operator
placement in distributed databases, and module placement in distributed
computing.
We first show that obtaining minimum-delay and minimum-cost embeddings are
both NP-complete problems and that cost minimization is actually MAX SNP-hard.
Next, we consider specific forms of the computation graph for which polynomial
time solutions are possible. When the computation graph is a tree, a polynomial
time algorithm to obtain the minimum delay embedding is described. Next, for
the case when the function is described by a layered graph we describe an
algorithm that obtains the minimum cost embedding in polynomial time. This
algorithm can also be used to obtain an approximation for delay minimization.
We then consider bounded treewidth computation graphs and give an algorithm to
obtain the minimum cost embedding in polynomial time
Edge Multiway Cut and Node Multiway Cut are NP-complete on subcubic graphs
We show that Edge Multiway Cut (also called Multiterminal Cut) and Node
Multiway Cut are NP-complete on graphs of maximum degree (also known as
subcubic graphs). This improves on a previous degree bound of . Our
NP-completeness result holds even for subcubic graphs that are planar
Tight Bounds for Gomory-Hu-like Cut Counting
By a classical result of Gomory and Hu (1961), in every edge-weighted graph
, the minimum -cut values, when ranging over all ,
take at most distinct values. That is, these instances
exhibit redundancy factor . They further showed how to construct
from a tree that stores all minimum -cut values. Motivated
by this result, we obtain tight bounds for the redundancy factor of several
generalizations of the minimum -cut problem.
1. Group-Cut: Consider the minimum -cut, ranging over all subsets
of given sizes and . The redundancy
factor is .
2. Multiway-Cut: Consider the minimum cut separating every two vertices of
, ranging over all subsets of a given size . The
redundancy factor is .
3. Multicut: Consider the minimum cut separating every demand-pair in
, ranging over collections of demand pairs. The
redundancy factor is . This result is a bit surprising, as
the redundancy factor is much larger than in the first two problems.
A natural application of these bounds is to construct small data structures
that stores all relevant cut values, like the Gomory-Hu tree. We initiate this
direction by giving some upper and lower bounds.Comment: This version contains additional references to previous work (which
have some overlap with our results), see Bibliographic Update 1.
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