Related papers: GraphCombEx: A Software Tool for Exploration of Co…
A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…
The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to…
Recently, there has been much work on the design of general heuristics for graph-based, combinatorial optimization problems via the incorporation of Graph Neural Networks (GNNs) to learn distribution-specific solution structures.However,…
Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and…
In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…
Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that…
The rapidly growing number of large network analysis problems has led to the emergence of many parallel and distributed graph processing systems---one survey in 2014 identified over 80. Since then, the landscape has evolved; some packages…
Finding frequently occurring subgraph patterns or network motifs in neural architectures is crucial for optimizing efficiency, accelerating design, and uncovering structural insights. However, as the subgraph size increases,…
Combinatorial optimization problems arise in a wide range of applications from diverse domains. Many of these problems are NP-hard and designing efficient heuristics for them requires considerable time and experimentation. On the other…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
Graph-structured data is ubiquitous throughout natural and social sciences, and Graph Neural Networks (GNNs) have recently been shown to be effective at solving prediction and inference problems on graph data. In this paper, we propose and…
Generating explanations for graph neural networks (GNNs) has been studied to understand their behavior in analytical tasks such as graph classification. Existing approaches aim to understand the overall results of GNNs rather than providing…
Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and…
Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as…
The advent of new special-purpose hardware such as FPGA or ASIC-based annealers and quantum processors has shown potential in solving certain families of complex combinatorial optimization problems more efficiently than conventional CPUs.…
Neural networks have been shown to be an effective tool for learning algorithms over graph-structured data. However, graph representation techniques---that convert graphs to real-valued vectors for use with neural networks---are still in…
In this paper, from a theoretical perspective, we study how powerful graph neural networks (GNNs) can be for learning approximation algorithms for combinatorial problems. To this end, we first establish a new class of GNNs that can solve a…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
Many problems can be presented in an abstract form through a wide range of binary objects and relations which are defined over problem domain. In these problems, graphical demonstration of defined binary objects and solutions is the most…