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We introduce and study four optimization problems that generalize the well-known subset sum problem. Given a node-weighted digraph, select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints…
One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions.…
This paper considers a generalization of the network design problem for On-Demand Multimodal Transit Systems (ODMTS). An ODMTS consists of a selection of hubs served by high frequency buses, and passengers are connected to the hubs by…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
The routing and wavelength assignment problem arises from the investigation of optimal wavelength allocation in an optical network that employs Wavelength Division Multiplexing (WDM). Consider an optical network that is represented by a…
The sorting number of a graph with $n$ vertices is the minimum depth of a sorting network with $n$ inputs and outputs that uses only the edges of the graph to perform comparisons. Many known results on sorting networks can be stated in…
Computer networks are the foundation of modern digital infrastructure, facilitating global communication and data exchange. As demand for reliable high-bandwidth connectivity grows, advanced network modeling techniques become increasingly…
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…
The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating…
Wireless network topologies change over time and maintaining routes requires frequent updates. Updates are costly in terms of consuming throughput available for data transmission, which is precious in wireless networks. In this paper, we…
The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics. Many hard computational problems on graphs turn out to be efficiently solvable in…
In this thesis we consider ordered graphs (that is, graphs with a fixed linear ordering on their vertices). We summarize and further investigations on the number of edges an ordered graph may have while avoiding a fixed forbidden ordered…
This paper provides an in-depth study of the fundamental problems of finding small subgraphs in distributed dynamic networks. While some problems are trivially easy to handle, such as detecting a triangle that emerges after an edge…
We tackle the problem of goal-directed graph construction: given a starting graph, a budget of modifications, and a global objective function, the aim is to find a set of edges whose addition to the graph achieves the maximum improvement in…
Given a digraph with two terminal vertices $s$ and $t$ as well as a conservative cost function and several not necessarily disjoint color classes on its arc set, our goal is to find a minimum-cost subset of the arcs such that its…
In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…
We propose and study a model of traffic in communication networks. The underlying network has a structure that is tunable between a scale-free growing network with preferential attachments and a random growing network. To model realistic…
A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. A dominating set is connected if the subgraph induced by its vertices is connected. The connected domatic partition problem asks for…