Related papers: A Compendium of Reductions: reductions.network
This thesis centers around the concept of Subset Search Problems (SSP), a type of computational problem introduced by Gr\"une and Wulf to analyze the complexity of more intricate optimization problems. These problems are given an input set,…
A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this…
Topological data analysis (TDA) delivers invaluable and complementary information on the intrinsic properties of data inaccessible to conventional methods. However, high computational costs remain the primary roadblock hindering the…
Confusing classes that are ubiquitous in real world often degrade performance for many vision related applications like object detection, classification, and segmentation. The confusion errors are not only caused by similar visual patterns…
Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this type of network, we intend to reduce the number of network…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final…
Modern data acquisition routinely produces massive amounts of network data. Though many methods and models have been proposed to analyze such data, the research of network data is largely disconnected with the classical theory of…
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the…
The contemporary scientific landscape is characterized by a "curse of dimensionality," where our capacity to collect high-dimensional network data frequently outstrips our ability to computationally simulate or intuitively comprehend the…
Graph neural networks (GNNs) have emerged as a powerful tool for solving combinatorial optimization problems (COPs), exhibiting state-of-the-art performance in both graph-structured and non-graph-structured domains. However, existing…
MapReduce (and its open source implementation Hadoop) has become the de facto platform for processing large data sets. MapReduce offers a streamlined computational framework by interleaving sequential and parallel computation while hiding…
Computer networks have been traditionally configured by humans using command-line interfaces. Some network abstractions have emerged in the last 10 years, but there is no easy way of comparing them to each other objectively. Therefore,…
Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
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 propose a new directed graphical representation of utility functions, called UCP-networks, that combines aspects of two existing graphical models: generalized additive models and CP-networks. The network decomposes a utility function…
The connectivity of a graph is an important parameter to evaluate its reliability. $k$-restricted connectivity (resp. $R^h$-restricted connectivity) of a graph $G$ is the minimum cardinality of a set $S$ of vertices in $G$, if exists, whose…
Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature,…
Constraint satisfaction problems (CSPs) are a class of problems that are ubiquitous in science and engineering. It features a collection of constraints specified over subsets of variables. A CSP can be solved either directly or by reducing…