Related papers: Biased landscapes for random Constraint Satisfacti…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…
The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…
Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in…
Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…
We investigate the Constraint Satisfaction Problem (CSP) over templates with a group structure, and algorithms solving CSP that are equivariant, i.e. invariant under a natural group action induced by a template. Our main result is a method…
We present an efficient algorithm to solve semirandom planted instances of any Boolean constraint satisfaction problem (CSP). The semirandom model is a hybrid between worst-case and average-case input models, where the input is generated by…
As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that…
Semi-supervised clustering methods incorporate a limited amount of supervision into the clustering process. Typically, this supervision is provided by the user in the form of pairwise constraints. Existing methods use such constraints in…
The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years. A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about…
Several recent unsupervised learning methods use probabilistic approaches to solve combinatorial optimization (CO) problems based on the assumption of statistically independent solution variables. We demonstrate that this assumption imposes…
Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and…
The Constraint Satisfaction Problem (CSP) is a problem of computing a homomorphism $\mathbf{R}\to \mathbf{\Gamma}$ between two relational structures, where $\mathbf{R}$ is defined over a domain $V$ and $\mathbf{\Gamma}$ is defined over a…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
Constrained clustering has been well-studied for algorithms such as $K$-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode…
Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…
Identifying clusters of similar objects in data plays a significant role in a wide range of applications. As a model problem for clustering, we consider the densest k-disjoint-clique problem, whose goal is to identify the collection of k…
In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…
What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called…