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The bipartite matching problem is widely applied in the field of transportation; e.g., to find optimal matches between supply and demand over time and space. Recent efforts have been made on developing analytical formulas to estimate the…
We show that the bipartite perfect matching problem is in quasi-NC$^2$. That is, it has uniform circuits of quasi-polynomial size $n^{O(\log n)}$, and $O(log^2 n)$ depth. Previously, only an exponential upper bound was known on the size of…
This results in this paper have been merged with the result in arXiv:1002.3763v1 The authors would like to withdraw this version. Please see arXiv:1008.5356v1 for the merged version.
Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…
Unfortunately, the article "A Comparative Study to Benchmark Cross-project Defect Prediction Approaches" has a problem in the statistical analysis which was pointed out almost immediately after the pre-print of the article appeared online.…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
We derive the leading exponential finite volume corrections in two dimensional integrable models for non-diagonal form factors in diagonally scattering theories. These formulas are expressed in terms of the infinite volume form factors and…
In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete even when restricted to bipartite graphs. It has been…
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…
We show that the principal results of the article "The metric dimension of graph with pendant edges" [Journal of Combinatorial Mathematics and Combinatorial Computing, 65 (2008) 139--145] do not hold. In this paper we correct the results…
In this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ram\'irez C., Math. Program. 104 (2005), no. 2-3, Ser. B,…
This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…
Here we prove that counting maximum matchings in planar, bipartite graphs is #P-complete. This is somewhat surprising in the light that the number of perfect matchings in planar graphs can be computed in polynomial time. We also prove that…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic…
Given a set of points in the plane, we are interested in matching them with straight line segments. We focus on perfect (all points are matched) non-crossing (no two edges intersect) matchings. Apart from the well known MinMax variation,…
Since their introduction, Boolean networks have been traditionally studied in view of their rich dynamical behavior under different update protocols and for their qualitative analogy with cell regulatory networks. More recently, tools…
Sorting algorithms have attracted a great deal of attention and study, as they have numerous applications to Mathematics, Computer Science and related fields. In this thesis, we first deal with the mathematical analysis of the Quicksort…
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…
Finite-size (FS) effects are a major source of error in many-body (MB) electronic structure calculations of extended systems. A method is presented to correct for such errors. We show that MB FS effects can be effectively included in a…