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We design quantum algorithms for maximum matching. Working in the query model, in both adjacency matrix and adjacency list settings, we improve on the best known algorithms for general graphs, matching previously obtained results for…
A typical problem in optimal design theory is finding an experimental design that is optimal with respect to some criteria in a class of designs. The most popular criteria include the A- and D-criteria. Regular graph designs occur in many…
The exploration of Graph Neural Networks (GNNs) for processing graph-structured data has expanded, particularly their potential for causal analysis due to their universal approximation capabilities. Anticipated to significantly enhance…
Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
We present new quantum algorithms for Triangle Finding improving its best previously known quantum query complexities for both dense and spare instances.For dense graphs on $n$ vertices, we get a query complexity of $O(n^{5/4})$ without any…
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…
Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at…
Many machine learning techniques have been proposed in the last few years to process data represented in graph-structured form. Graphs can be used to model several scenarios, from molecules and materials to RNA secondary structures. Several…
``Algorithms with predictions'', or ``learning-augmented algorithms'', has proved to be an extremely useful paradigm for combining machine learning with traditional algorithms. One of the textbook settings for this is searching a sorted…
Knowledge Graphs are increasingly becoming popular for a variety of downstream tasks like Question Answering and Information Retrieval. However, the Knowledge Graphs are often incomplete, thus leading to poor performance. As a result, there…
Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks,…
Graph Neural Networks (GNNs) have emerged as a powerful tool for learning from graph-structured data. However, even state-of-the-art architectures have limitations on what structures they can distinguish, imposing theoretical limits on what…
We propose a combinatorial optimisation model called Limited Query Graph Connectivity Test. We consider a graph whose edges have two possible states (On/Off). The edges' states are hidden initially. We could query an edge to reveal its…
Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity…
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…
Graph neural networks (GNN) has been successfully applied to operate on the graph-structured data. Given a specific scenario, rich human expertise and tremendous laborious trials are usually required to identify a suitable GNN architecture.…
Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…
Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level…
The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations forprobabilistic…