Related papers: Efficient Enumeration of the Optimal Solutions to …
We present a novel local improvement scheme for the perfectly balanced graph partitioning problem. This scheme encodes local searches that are not restricted to a balance constraint into a model allowing us to find combinations of these…
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…
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…
Spectral clustering methodologies, when extended to accommodate signed graphs, have encountered notable limitations in effectively encapsulating inherent grouping relationships. Recent findings underscore a substantial deterioration in the…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
In this paper, we reduce the complexity of approximating the correlation clustering problem from $O(m\times\left( 2+ \alpha (G) \right)+n)$ to $O(m+n)$ for any given value of $\varepsilon$ for a complete signed graph with $n$ vertices and…
Signed networks are graphs whose edges are labelled with either a positive or a negative sign, and can be used to capture nuances in interactions that are missed by their unsigned counterparts. The concept of balance in signed graph theory…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
We propose new mathematical programming models for optimal partitioning of a signed graph into cohesive groups. To demonstrate the approach's utility, we apply it to identify coalitions in US Congress since 1979 and examine the impact of…
The Correlation Clustering problem is one of the most extensively studied clustering formulations due to its wide applications in machine learning, data mining, computational biology and other areas. We consider the Correlation Clustering…
We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…
Several clustering frameworks with interactive (semi-supervised) queries have been studied in the past. Recently, clustering with same-cluster queries has become popular. An algorithm in this setting has access to an oracle with full…
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: $+$…
We analyse signed networks from the perspective of balance theory which predicts structural balance as a global structure for signed social networks that represent groups of friends and enemies. The scarcity of balanced networks encouraged…
In the correlation clustering problem for complete signed graphs, the input is a complete signed graph with edges weighted as $+1$ (denote recommendation to put this pair in the same cluster) or $-1$ (recommending to put this pair of…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…