We design efficient deterministic algorithms for finding short edge-disjoint paths in expanders. Specifically, given an \(n\)-vertex \(m\)-edge expander \(G\) of conductance \(\phi\) and minimum degree \(\delta\), and a set of pairs \(\{(s_i,t_i)\}_i\) such that each vertex appears in at most \(k\) pairs, our algorithm deterministically computes a set of edge-disjoint paths from \(s_i\) to \(t_i\), one for every \(i\): (1) each of length at most \(18 \log(n)/\phi\) and in \(mn^{1+o(1)} \min\{k,\phi^{-1}\}\) total time, assuming \(\phi^3 \delta \ge (35 \log n)^3 k\), or (2) each of length at most \(n^{o(1)}/\phi\) and in total \(m^{1+o(1)}\) time, assuming \(\phi^3 \delta \ge n^{o(1)} k\). Before our work, deterministic polynomial-time algorithms were known only for expanders with constant conductance and were significantly slower. To obtain our result, we give an almost-linear time algorithm for hypergraph perfect matching under generalizations of Hall-type conditions (Haxell 1995), a powerful framework with applications in various settings, which until now has only admitted large polynomial-time algorithms (Annamalai 2018).

Remote photoplethysmography (rPPG) is a non-contact method that detects blood volume changes in facial tissues from video. The non-invasiveness of rPPG makes it promising for applications in remote health monitoring and telemedicine. However, its real-world application is hindered by a fundamental challenge. Existing models are typically designed for high-resolution, fixed-size inputs, making them ill-suited for the arbitrary-resolution videos commonly encountered in practical scenarios due to dynamic camera-to-subject distances. To address this challenge, we propose ResoPhys, an unsupervised plug-and-play rPPG measurement method designed for facial videos of arbitrary resolution. This method first generates video pairs via random scaling and then employs specialized modules for arbitrary-resolution feature extraction and upsampling to analyze the resulting multi-scale features. The framework is optimized via an unsupervised contrastive learning approach using our proposed multi-resolution contrastive loss. To validate its performance across a spectrum of resolutions, we evaluated ResoPhys on several public datasets. The results demonstrate the superiority of our method over previous unsupervised approaches, exhibiting particular strength in challenging low-resolution scenarios, which underscores its robustness to resolution changes. Crucially, ResoPhys acts as a universal front-end that decouples resolution handling from signal extraction, empowering existing rPPG networks for effective deployment in arbitrary-resolution conditions.

The network coding problem asks whether data throughput in a network can be increased using coding (compared to treating bits as commodities in a flow). While it is well-known that a network coding advantage exists in directed graphs, the situation in undirected graphs is much less understood – in particular, despite significant effort, it is not even known whether network coding is helpful at all for unicast sessions.In this paper we study the multi-source multicast network coding problem in undirected graphs. There are k sources broadcasting each to a subset of nodes in a graph of size n. The corresponding combinatorial problem is a version of the Steiner tree packing problem, and the network coding question asks whether the multicast coding rate exceeds the tree-packing rate.We give the first super–constant bound to this problem, demonstrating an example with a coding advantage of $\Omega(\log k)$. In terms of graph size, we obtain a lower bound of $2^{\tilde{\Omega}(\sqrt{\log \log n})}$. We also obtain an upper bound of $O(\log n)$ on the gap.Our main technical contribution is a new reduction that converts locally-decodable codes in the low-error regime into multicast coding instances. This gives rise to a new family of explicitly constructed graphs, which may have other applications.

A cactus representation of a graph, introduced by Dinitz et al. in 1976, is an edge sparsifier of O(n) size that exactly captures all global minimum cuts of the graph. It is a central combinatorial object that has been a key ingredient in almost all algorithms for the connectivity augmentation problems and for maintaining minimum cuts under edge insertions (e.g. [Naor et al. SICOMP’97], [Cen et al. SODA’22], [Henzinger ICALP’95]). This sparsifier was generalized to Steiner cactus for a vertex set T, which can be seen as a vertex sparsifier of O(|T|) size that captures all partitions of T corresponding to a T-Steiner minimum cut, and also hypercactus, an analogous concept in hypergraphs. These generalizations further extend the applications of cactus to the Steiner and hypergraph settings.

Given an undirected weighted graph with n vertices and m edges, we give the first deterministic m1+o(1)-time algorithm for constructing the cactus representation of all global minimum cuts. This improves the current n2+o(1)-time state-of-the-art deterministic algorithm, which can be obtained by combining ideas implicitly from three papers [22, 27, 12]. The known explicitly stated deterministic algorithm has a runtime of Õ(mn) [9, 34]. Using our technique, we can even speed up the fastest randomized algorithm of [23] whose running time is at least Ω(m log4 n) to O(m log3 n).

This paper studies online correlated selection (OCS). Suppose that we receive a pair of elements in each round and select one of them. Can we select with negative correlation to be more effective than independent random selections? Our contributions are threefold. For semi-OCS, which considers the probability that an element remains unselected after appearing in$k$rounds, we give an optimal algorithm that minimizes this probability for all k. It leads to 0.536-competitive unweighted and vertex-weighted on-line bipartite matching algorithms that randomize over only two options in each round, improving the previous 0.508-competitive ratio by Fahrbach et al. (2020). Further, we develop the first multi-way semi-OCS that allows an arbitrary number of elements with arbitrary masses in each round. As an application, it rounds the Balance algorithm in unweighted and vertex-weighted online bi-partite matching to get a 0.593-competitive ratio. Finally, we study OCS, which further considers the probability that an element is unselected in any subset of rounds. We prove that the optimal “level of negative correlation” is between 0.167 and 0.25, improving the previous bounds of 0.109 and 1 by Fahrbach et al. (2020). Our OCS gives a 0.519-competitive edge-weighted online bipartite matching algorithm, improving the previous 0.508-competitive ratio by Fahrbach et al. (2020).

Web databases are now pervasive. Such a database can be accessed via its query interface (usually HTML query form) only. Extracting Web query interfaces is a critical step in data integration across multiple Web databases, which creates a formal representation of a query form by extracting a set of query conditions in it. This paper presents a novel approach to extracting Web query interfaces. In this approach, a generic set of query condition rules are created to define query conditions that are semantically equivalent to SQL search conditions. Query condition rules represent the semantic roles that labels and form elements play in query conditions, and how they are hierarchically grouped into constructs of query conditions. To group labels and form elements in a query form, we explore both their structural proximity in the hierarchy of structures in the query form, which is captured by a tree of nested tags in the HTML codes of the form, and their semantic similarity, which is captured by various short texts used in labels, form elements and their properties. We have implemented the proposed approach and our experimental results show that the approach is highly effective.