Related papers: Worst-Case to Expander-Case Reductions: Derandomiz…
Expander decompositions have become one of the central frameworks in the design of fast algorithms. For an undirected graph $G=(V,E)$, a near-optimal $\phi$-expander decomposition is a partition $V_1, V_2, \ldots, V_k$ of the vertex set $V$…
Invertible transformation of large graphs into fixed dimensional vectors (embeddings) remains a challenge. Its overcoming would reduce any operation on graphs to an operation in a vector space. However, most existing methods are limited to…
Graph neural networks, a powerful deep learning tool to model graph-structured data, have demonstrated remarkable performance on numerous graph learning tasks. To address the data noise and data scarcity issues in deep graph learning, the…
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the…
As large-scale graphs become increasingly more prevalent, it poses significant computational challenges to process, extract and analyze large graph data. Graph coarsening is one popular technique to reduce the size of a graph while…
An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…
Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral…
We introduce a unified framework based on bi-level optimization schemes to deal with parameter learning in the context of image processing. The goal is to identify the optimal regularizer within a family depending on a parameter in a…
The classic technique of Baker [J. ACM '94] is the most fundamental approach for designing approximation schemes on planar, or more generally topologically-constrained graphs, and it has been applied in a myriad of different variants and…
In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real--world instances. The model is more flexible than the semi-random model of Feige and Kilian and…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
The Isolation Lemma of Mulmuley, Vazirani and Vazirani [Combinatorica'87] provides a self-reduction scheme that allows one to assume that a given instance of a problem has a unique solution, provided a solution exists at all. Since its…
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 expansion of a hypergraph, a natural extension of the notion of expansion in graphs, is defined as the minimum over all cuts in the hypergraph of the ratio of the number of the hyperedges cut to the size of the smaller side of the cut.…
In machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
Dense subgraph discovery is an important problem in graph mining and network analysis with several applications. Two canonical problems here are to find a maxcore (subgraph of maximum min degree) and to find a densest subgraph (subgraph of…
We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…
We propose a scalable framework for solving the Maximum Cut (MaxCut) problem in large graphs using projected gradient ascent on quadratic objectives. Our approach is differentiable and leverages GPUs for gradient-based optimization. It is…
While promising, graph reasoners based on Large Language Models (LLMs) lack built-in invariance to symmetries in graph representations. Operating on sequential graph serializations, LLMs can produce different outputs under node reindexing,…