Related papers: A $k$-medoids Approach to Exploring Districting Pl…
This paper presents a feature level fusion approach which uses the improved K-medoids clustering algorithm and isomorphic graph for face and palmprint biometrics. Partitioning around medoids (PAM) algorithm is used to partition the set of n…
The boundaries of electoral constituencies for assembly and parliamentary seats are drafted using a process referred to as delimitation, which ensures fair and equal representation of all citizens. The current delimitation exercise suffers…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
Gerrymandering is a practice of manipulating district boundaries and locations in order to achieve a political advantage for a particular party. Lewenberg, Lev, and Rosenschein [AAMAS 2017] initiated the algorithmic study of a…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
Redistricting practitioners must balance many competing constraints and criteria when drawing district boundaries. To aid in this process, researchers have developed many methods for optimizing districting plans according to one or more…
Finding communities in graphs is one of the most well-studied problems in data mining and social-network analysis. In many real applications, the underlying graph does not have a clear community structure. In those cases, selecting a single…
An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard,…
A widely-used operation on graphs is local clustering, i.e., extracting a well-characterized community around a seed node without the need to process the whole graph. Recently local motif clustering has been proposed: it looks for a local…
Every representative democracy must specify a mechanism under which voters choose their representatives. The most common mechanism in the United States -- Winner takes all single-member districts -- both enables substantial partisan…
The gerrymandering problem is a worldwide problem which sets great threat to democracy and justice in district based elections. Thanks to partisan redistricting commissions, district boundaries are often manipulated to benefit incumbents.…
We develop an algorithm for i) computing generalized regular $k$-point grids, ii) reducing the grids to their symmetrically distinct points, and iii) mapping the reduced grid points into the Brillouin zone. The algorithm exploits the…
We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
Normalized-cut graph partitioning aims to divide the set of nodes in a graph into $k$ disjoint clusters to minimize the fraction of the total edges between any cluster and all other clusters. In this paper, we consider a fair variant of the…
We compare different analytical and numerical methods for studying the partitions of a finite system into fragments. We propose a new numerical method of exploring the partition space by generating the Markov chains of partitions based on…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Densest subgraph discovery (DSD) is a fundamental problem in graph mining. It has been studied for decades, and is widely used in various areas, including network science, biological analysis, and graph databases. Given a graph G, DSD aims…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…