1,491 research outputs found
Finding Stable Matchings That Are Robust to Errors in the Input
In this paper, we introduce the issue of finding solutions to the stable matching problem that are robust to errors in the input and we obtain the first algorithmic results on this topic. In the process, we also initiate work on a new structural question concerning the stable matching problem, namely finding relationships between the lattices of solutions of two "nearby" instances.
Our main algorithmic result is the following: We identify a polynomially large class of errors, D, that can be introduced in a stable matching instance. Given an instance A of stable matching, let B be the instance that results after introducing one error from D, chosen via a discrete probability distribution. The problem is to find a stable matching for A that maximizes the probability of being stable for B as well. Via new structural properties of the type described in the question stated above, we give a polynomial time algorithm for this problem
A Structural and Algorithmic Study of Stable Matching Lattices of Multiple Instances
Recently MV18a identified and initiated work on the new problem of
understanding structural relationships between the lattices of solutions of two
``nearby'' instances of stable matching. They also gave an application of their
work to finding a robust stable matching. However, the types of changes they
allowed in going from instance to were very restricted, namely, any one
agent executes an upward shift.
In this paper, we allow any one agent to permute its preference list
arbitrarily. Let and be the sets of stable matchings of the
resulting pair of instances and , and let and
be the corresponding lattices of stable matchings. We prove
that the matchings in form a sublattice of both
and and those in form a join
semi-sublattice of . These properties enable us to obtain a
polynomial time algorithm for not only finding a stable matching in , but also for obtaining the partial order, as promised by Birkhoff's
Representation Theorem, thereby enabling us to generate all matchings in this
sublattice.
Our algorithm also helps solve a version of the robust stable matching
problem. We discuss another potential application, namely obtaining new
insights into the incentive compatibility properties of the Gale-Shapley
Deferred Acceptance Algorithm.Comment: arXiv admin note: substantial text overlap with arXiv:1804.0553
Stable Matching with Evolving Preferences
We consider the problem of stable matching with dynamic preference lists. At
each time step, the preference list of some player may change by swapping
random adjacent members. The goal of a central agency (algorithm) is to
maintain an approximately stable matching (in terms of number of blocking
pairs) at all times. The changes in the preference lists are not reported to
the algorithm, but must instead be probed explicitly by the algorithm. We
design an algorithm that in expectation and with high probability maintains a
matching that has at most blocking pairs.Comment: 13 page
Robust Non-Rigid Registration with Reweighted Position and Transformation Sparsity
Non-rigid registration is challenging because it is ill-posed with high
degrees of freedom and is thus sensitive to noise and outliers. We propose a
robust non-rigid registration method using reweighted sparsities on position
and transformation to estimate the deformations between 3-D shapes. We
formulate the energy function with position and transformation sparsity on both
the data term and the smoothness term, and define the smoothness constraint
using local rigidity. The double sparsity based non-rigid registration model is
enhanced with a reweighting scheme, and solved by transferring the model into
four alternately-optimized subproblems which have exact solutions and
guaranteed convergence. Experimental results on both public datasets and real
scanned datasets show that our method outperforms the state-of-the-art methods
and is more robust to noise and outliers than conventional non-rigid
registration methods.Comment: IEEE Transactions on Visualization and Computer Graphic
Simultaneous identification of specifically interacting paralogs and inter-protein contacts by Direct-Coupling Analysis
Understanding protein-protein interactions is central to our understanding of
almost all complex biological processes. Computational tools exploiting rapidly
growing genomic databases to characterize protein-protein interactions are
urgently needed. Such methods should connect multiple scales from evolutionary
conserved interactions between families of homologous proteins, over the
identification of specifically interacting proteins in the case of multiple
paralogs inside a species, down to the prediction of residues being in physical
contact across interaction interfaces. Statistical inference methods detecting
residue-residue coevolution have recently triggered considerable progress in
using sequence data for quaternary protein structure prediction; they require,
however, large joint alignments of homologous protein pairs known to interact.
The generation of such alignments is a complex computational task on its own;
application of coevolutionary modeling has in turn been restricted to proteins
without paralogs, or to bacterial systems with the corresponding coding genes
being co-localized in operons. Here we show that the Direct-Coupling Analysis
of residue coevolution can be extended to connect the different scales, and
simultaneously to match interacting paralogs, to identify inter-protein
residue-residue contacts and to discriminate interacting from noninteracting
families in a multiprotein system. Our results extend the potential
applications of coevolutionary analysis far beyond cases treatable so far.Comment: Main Text 19 pages Supp. Inf. 16 page
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