3,205 research outputs found
Some complexity and approximation results for coupled-tasks scheduling problem according to topology
We consider the makespan minimization coupled-tasks problem in presence of
compatibility constraints with a specified topology. In particular, we focus on
stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution
time and idle time duration. We study several problems in framework of classic
complexity and approximation for which the compatibility graph is bipartite
(star, chain,. . .). In such a context, we design some efficient
polynomial-time approximation algorithms for an intractable scheduling problem
according to some parameters
Extended modular operad
This paper is a sequel to [LoMa] where moduli spaces of painted stable curves
were introduced and studied. We define the extended modular operad of genus
zero, algebras over this operad, and study the formal differential geometric
structures related to these algebras: pencils of flat connections and Frobenius
manifolds without metric. We focus here on the combinatorial aspects of the
picture. Algebraic geometric aspects are treated in [Ma2].Comment: 38 pp., amstex file, no figures. This version contains additional
references and minor change
A closed-form approach to Bayesian inference in tree-structured graphical models
We consider the inference of the structure of an undirected graphical model
in an exact Bayesian framework. More specifically we aim at achieving the
inference with close-form posteriors, avoiding any sampling step. This task
would be intractable without any restriction on the considered graphs, so we
limit our exploration to mixtures of spanning trees. We consider the inference
of the structure of an undirected graphical model in a Bayesian framework. To
avoid convergence issues and highly demanding Monte Carlo sampling, we focus on
exact inference. More specifically we aim at achieving the inference with
close-form posteriors, avoiding any sampling step. To this aim, we restrict the
set of considered graphs to mixtures of spanning trees. We investigate under
which conditions on the priors - on both tree structures and parameters - exact
Bayesian inference can be achieved. Under these conditions, we derive a fast an
exact algorithm to compute the posterior probability for an edge to belong to
{the tree model} using an algebraic result called the Matrix-Tree theorem. We
show that the assumption we have made does not prevent our approach to perform
well on synthetic and flow cytometry data
Combinatorics and geometry of finite and infinite squaregraphs
Squaregraphs were originally defined as finite plane graphs in which all
inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e.,
the vertices not incident with the outer face) have degrees larger than three.
The planar dual of a finite squaregraph is determined by a triangle-free chord
diagram of the unit disk, which could alternatively be viewed as a
triangle-free line arrangement in the hyperbolic plane. This representation
carries over to infinite plane graphs with finite vertex degrees in which the
balls are finite squaregraphs. Algebraically, finite squaregraphs are median
graphs for which the duals are finite circular split systems. Hence
squaregraphs are at the crosspoint of two dualities, an algebraic and a
geometric one, and thus lend themselves to several combinatorial
interpretations and structural characterizations. With these and the
5-colorability theorem for circle graphs at hand, we prove that every
squaregraph can be isometrically embedded into the Cartesian product of five
trees. This embedding result can also be extended to the infinite case without
reference to an embedding in the plane and without any cardinality restriction
when formulated for median graphs free of cubes and further finite
obstructions. Further, we exhibit a class of squaregraphs that can be embedded
into the product of three trees and we characterize those squaregraphs that are
embeddable into the product of just two trees. Finally, finite squaregraphs
enjoy a number of algorithmic features that do not extend to arbitrary median
graphs. For instance, we show that median-generating sets of finite
squaregraphs can be computed in polynomial time, whereas, not unexpectedly, the
corresponding problem for median graphs turns out to be NP-hard.Comment: 46 pages, 14 figure
Paired and altruistic kidney donation in the UK: algorithms and experimentation
We study the computational problem of identifying optimal
sets of kidney exchanges in the UK. We show how to expand an integer
programming-based formulation [1, 19] in order to model the criteria that
constitute the UK definition of optimality. The software arising from this
work has been used by the National Health Service Blood and Transplant
to find optimal sets of kidney exchanges for their National Living Donor
Kidney Sharing Schemes since July 2008.We report on the characteristics
of the solutions that have been obtained in matching runs of the scheme
since this time. We then present empirical results arising from the real
datasets that stem from these matching runs, with the aim of establishing
the extent to which the particular optimality criteria that are present
in the UK influence the structure of the solutions that are ultimately
computed. A key observation is that allowing 4-way exchanges would be
likely to lead to a significant number of additional transplants
A comonadic view of simulation and quantum resources
We study simulation and quantum resources in the setting of the
sheaf-theoretic approach to contextuality and non-locality. Resources are
viewed behaviourally, as empirical models. In earlier work, a notion of
morphism for these empirical models was proposed and studied. We generalize and
simplify the earlier approach, by starting with a very simple notion of
morphism, and then extending it to a more useful one by passing to a co-Kleisli
category with respect to a comonad of measurement protocols. We show that these
morphisms capture notions of simulation between empirical models obtained via
`free' operations in a resource theory of contextuality, including the type of
classical control used in measurement-based quantum computation schemes.Comment: To appear in Proceedings of LiCS 201
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