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Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
Designing dynamic graph algorithms against an adaptive adversary is a major goal in the field of dynamic graph algorithms. While a few such algorithms are known for spanning trees, matchings, and single-source shortest paths, very little…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
Infrastructure monitoring is critical for safe operations and sustainability. Water distribution networks (WDNs) are large-scale networked critical systems with complex cascade dynamics which are difficult to predict. Ubiquitous monitoring…
Networked dynamic systems are ubiquitous in various domains, such as industrial processes, social networks, and biological systems. These systems produce high-dimensional data that reflect the complex interactions among the network nodes…
Truss was proposed to study social network data represented by graphs. A k-truss of a graph is a cohesive subgraph, in which each edge is contained in at least k-2 triangles within the subgraph. While truss has been demonstrated as superior…
Many robotic exploration algorithms rely on graph structures for frontier-based exploration and dynamic path planning. However, these graphs grow rapidly, accumulating redundant information and impacting performance. We present a…
Maintaining and updating shortest paths information in a graph is a fundamental problem with many applications. As computations on dense graphs can be prohibitively expensive, and it is preferable to perform the computations on a sparse…
We give two fully dynamic algorithms that maintain a $(1+\varepsilon)$-approximation of the weight $M$ of a minimum spanning forest (MSF) of an $n$-node graph $G$ with edges weights in $[1,W]$, for any $\varepsilon>0$. (1) Our deterministic…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
We consider the classic facility location problem in fully dynamic data streams, where elements can be both inserted and deleted. In this problem, one is interested in maintaining a stable and high quality solution throughout the data…
Connectivity structure shapes neural computation, but inferring this structure from population recordings is degenerate: multiple connectivity structures can generate identical dynamics. Recent work uses low-rank recurrent neural networks…
We give a new data structure for the fully-dynamic minimum spanning forest problem in simple graphs. Edge updates are supported in $O(\log^4n/\log\log n)$ amortized time per operation, improving the $O(\log^4n)$ amortized bound of Holm et…
A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers certain queries that are specific to the problem under consideration. There has been a lot of research on dynamic algorithms…
A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…
Classic dynamic data structure problems maintain a data structure subject to a sequence S of updates and they answer queries using the latest version of the data structure, i.e., the data structure after processing the whole sequence. To…
We present the first non-trivial fully dynamic algorithm maintaining exact single-source distances in unweighted graphs. This resolves an open problem stated by Sankowski [COCOON 2005] and van den Brand and Nanongkai [FOCS 2019]. Previous…
Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by…
Water Distribution Networks (WDNs) are critical infrastructures that ensure safe drinking water. One of the major threats is the accidental or intentional injection of pollutants. Data collection remains challenging in underground WDNs and…
Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which…