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We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…
Modularity is a key organizing principle in real-world large-scale complex networks. Many real-world networks exhibit modular structures such as transportation infrastructures, communication networks and social media. Having the knowledge…
A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…
An isometric path between two vertices in a graph G is a shortest path joining them. The isometric-path number of G, denoted by ip(G), is the minimum number of isometric paths required to cover all vertices of G. In this paper, we determine…
Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
The hypergraph minimum cut problem aims to partition its vertices into two blocks while minimizing the total weight of the cut hyperedges. This fundamental problem arises in network reliability, VLSI design, and community detection. We…
Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for…
We consider a discrete-time linear-quadratic Gaussian control problem in which we minimize a weighted sum of the directed information from the state of the system to the control input and the control cost. The optimal control and sensing…
Small world models are networks consisting of many local links and fewer long range 'shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
Based upon the idea that network functionality is impaired if two nodes in a network are sufficiently separated in terms of a given metric, we introduce two combinatorial \emph{pseudocut} problems generalizing the classical min-cut and…
Generalized subtour elimination constraints (GSECs) are widely used in state-of-the-art exact algorithms for vehicle routing and network design problems, as their right-hand sides often capture problem-specific feasibility conditions of…
Motivated by an important insight from neural science, we propose a new framework for understanding the success of the recently proposed "maxout" networks. The framework is based on encoding information on sparse pathways and recognizing…
Given a graph $G$ and two vertices $s$ and $t$ in it, {\em graph reachability} is the problem of checking whether there exists a path from $s$ to $t$ in $G$. We show that reachability in directed layered planar graphs can be decided in…
Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…
Geodesic paths and distances are among the most popular intrinsic properties of 3D surfaces. Traditionally, geodesic paths on discrete polygon surfaces were computed using shortest path algorithms, such as Dijkstra. However, such algorithms…
This paper presents a novel approach to computing vector road maps from satellite remotely sensed images, building upon a well-defined Patched Line Segment (PaLiS) representation for road graphs that holds geometric significance. Unlike…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…