Related papers: Enumeration of Matchings: Problems and Progress
This PhD thesis is organized as follows. In the first two chapters I will review some basic notions of statistical physics of disordered systems, such as random graph theory, the mean-field approximation, spin glasses and combinatorial…
We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete
We reprove that all the matchings constructed during Edmonds' weighted perfect matching algorithm are optimal among those of the same cardinality (provided that certain mild restrictions are obeyed on the choices the algorithm makes). We…
The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known…
Context. Since the eighties, the combination of program analysis techniques has been increasingly recognized as a promising approach to overcome the limitations of standalone methods. While individual techniques, based on either static or…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
This is a survey of old and new problems and results in additive number theory.
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
This very preliminary text is related to ``Algorithms on Texts'', also called ``Algorithmic Stringology''. It is an extension of the book ``125 Problems in Text Algorithms'' providing, in the same compact style, more problems with…
This review describes the history of discovery of violation of spatial parity P, charge conjugation parity C, combined parity CP. The hypothesis of existence of mirror particles was called upon by its authors to restore the symmetry between…
A non-crossing pairing on a bitstring matches 1s and 0s in a manner such that the pairing diagram is nonintersecting. By considering such pairings on arbitrary bitstrings $1^{n_1} 0^{m_1} ... 1^{n_r} 0^{m_r}$, we generalize classical…
A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks. Here, we show an advance in the methodology of enumeration, making the process thousands or millions of…
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
The main contribution of this paper resides in developing a new algorithmic approach for addressing the continuous-time joint replenishment problem, termed $\Psi$-pairwise alignment. The latter mechanism, through which we synchronize…
In this paper, we present a new way of matching in observational studies that overcomes three limitations of existing matching approaches. First, it directly balances covariates with multi-valued treatments without requiring the generalized…
The clustering problem has many applications in Machine Learning, Operations Research, and Statistics. We propose three algorithms to create starting solutions for improvement algorithms for this problem. We test the algorithms on 72…
We survey $k$-best enumeration problems and the algorithms for solving them, including in particular the problems of finding the $k$ shortest paths, $k$ smallest spanning trees, and $k$ best matchings in weighted graphs.
We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…
We provide a geometric formulation of the problem of identification of the matching surplus function and we show how the estimation problem can be solved by the introduction of a generalized entropy function over the set of matchings.
This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of…