Related papers: Removing Popular Faces in Curve Arrangements
We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of…
Our input is a directed, rooted graph $G = (V \cup \{r\},E)$ where each vertex in $V$ has a partial order preference over its incoming edges. The preferences of a vertex extend naturally to preferences over arborescences rooted at $r$. We…
Let $P$ be a polygonal curve in $\mathbb{R}^D$ of length $n$, and $S$ be a point set of size $k$. The Curve/Point Set Matching problem consists of finding a polygonal curve $Q$ on $S$ such that its Fr\'echet distance from $P$ is less than a…
We study the Popular Matching problem in multiple models, where the preferences of the agents in the instance may change or may be unknown/uncertain. In particular, we study an Uncertainty model, where each agent has a possible set of…
Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…
Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…
We consider the many-to-many bipartite matching problem in the presence of two-sided preferences and two-sided lower quotas. The input to our problem is a bipartite graph G=(A U B, E), where each vertex in A U B specifies a strict…
Popular matchings provide a model of matching under preferences in which a solution corresponds to a Condorcet winner in voting systems. In a bipartite graph in which the vertices have preferences over their neighbours, a matching is…
Face clustering is an essential task in computer vision due to the explosion of related applications such as augmented reality or photo album management. The main challenge of this task lies in the imperfectness of similarities among image…
The Cluster Editing problem seeks a transformation of a given undirected graph into a disjoint union of cliques via a minimum number of edge additions or deletions. A multi-parameterized version of the problem is studied, featuring a number…
The perception of facial beauty is a complex phenomenon depending on many, detailed and global facial features influencing each other. In the machine learning community this problem is typically tackled as a problem of supervised inference.…
An arrangement of curves in the real plane divides it into a collection of faces. In the case of line arrangements, there exists an associative product which gives this collection a structure of a left regular band. A natural question is…
An arrangement of pseudocircles is a collection of simple closed curves on the sphere or in the plane such that any two of the curves are either disjoint or intersect in exactly two crossing points. We call an arrangement intersecting if…
We consider the problem of face swapping in images, where an input identity is transformed into a target identity while preserving pose, facial expression, and lighting. To perform this mapping, we use convolutional neural networks trained…
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
Given a point set, mostly a grid in our case, we seek upper and lower bounds on the number of curves that are needed to cover the point set. We say a curve covers a point if the curve passes through the point. We consider such coverings by…
A quadric in $\R P^3$ cuts a curve of degree 6 on a cubic surface in $\R P^3$. The papers classifies the nonsingular curves cut in this way on non-singular cubic surfaces up to homeomorphism. Two issues new in the study related to the first…
We consider the cheating strategies for the popular matchings problem. The popular matchings problem can be defined as follows: Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and the edges…
A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the…