# Algorithms & Complexity Breakthroughs Domain: Mathematics & Theoretical Computer Science · 192 papers indexed · newest 2026-10-25 Almost-linear-time max flow, shortest paths beyond Dijkstra's sorting barrier, matrix multiplication exponent improvements and space-time simulation results. Key concepts: almost-linear time, maximum flow, shortest paths, matrix multiplication, sorting barrier, time-space ## Most influential - **[Droplet formation and breakup dynamics in microfluidic flow-focusing devices: From dripping to jetting](https://space-kitty.com/papers/doi:10.1016/j.ces.2012.08.039)**. Taotao Fu, Yining Wu, Youguang Ma et al. · 2012 · Chemical Engineering Science (doi:10.1016/j.ces.2012.08.039 · 313 citations). Source: - **[Stomatal Function across Temporal and Spatial Scales: Deep-Time Trends, Land-Atmosphere Coupling and Global Models](https://space-kitty.com/papers/doi:10.1104/pp.17.00287)**. Peter J. Franks, Joseph A. Berry, Danica Lombardozzi et al. · 2017 · PLANT PHYSIOLOGY (doi:10.1104/pp.17.00287 · 159 citations). Source: > The colonization of land by plants and their interaction with biogeochemical and atmospheric processes transformed continental climate and hydrology. Stomata, which evolved to optimize the biological economics of plant carbon uptake in exchange for water loss, play a crucial role in large-scale environmental processes by maintaining a connection between deep soil water reservoirs and the atmosphere, regulating terrestrial carbon sinks and altering surface energy balance as they respond to environmental changes. Stomatal feedback control of leaf gas exchange is observed at multiple temporal and… > _Abstract excerpt by Peter J. Franks et al., CC-BY, https://doi.org/10.1104/pp.17.00287; truncated._ - **[A thermodynamic approach to link self-organization, preferential flow and rainfall–runoff behaviour](https://space-kitty.com/papers/doi:10.5194/hess-17-4297-2013)**. Erwin Zehe, Uwe Ehret, Theresa Blume et al. · 2013 · Hydrology and earth system sciences (doi:10.5194/hess-17-4297-2013 · 80 citations). Source: > Abstract. This study investigates whether a thermodynamically optimal hillslope structure can, if existent, serve as a first guess for uncalibrated predictions of rainfall–runoff. To this end we propose a thermodynamic framework to link rainfall–runoff processes and dynamics of potential energy, kinetic energy and capillary binding energy in catchments and hillslopes. The starting point is that hydraulic equilibrium in soil corresponds to local thermodynamic equilibrium (LTE), characterized by a local maximum entropy/minimum of free energy of soil water. Deviations from LTE occur either due to… > _Abstract excerpt by Erwin Zehe et al., CC-BY, https://doi.org/10.5194/hess-17-4297-2013; truncated._ - **[Closed loop supply chain networks: Designs for energy and time value efficiency](https://space-kitty.com/papers/doi:10.1016/j.ijpe.2016.02.004)**. Dinesh K. Kadambala, Nachiappan Subramanian, Manoj Kumar Tiwari et al. · 2016 · International Journal of Production Economics (doi:10.1016/j.ijpe.2016.02.004 · 79 citations). Source: - **[Fast Approximate Shortest Paths in the Congested Clique](https://space-kitty.com/papers/arxiv:1903.05956)**. Keren Censor-Hillel, Michal Dory, Janne H. Korhonen et al. · 2019 · Distributed Computing (arXiv:1903.05956 · doi:10.1007/s00446-020-00380-5 · 43 citations). Source: > We design fast deterministic algorithms for distance computation in the congested clique model. Our key contributions include: -- A $(2+ε)$-approximation for all-pairs shortest paths in $O(\\log^2{n} / ε)$ rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. -- A $(1+ε)$-approximation for multi-source shortest paths from $O(\\sqrt{n})$ sources in $O(\\log^2{n} / ε)$ rounds on weighted undirected graphs. This is the first sub-polynomial algorithm… - **[CUDA programs for solving the time-dependent dipolar Gross–Pitaevskii equation in an anisotropic trap](https://space-kitty.com/papers/arxiv:1601.04640)**. Vladimir Lončar, Antun Balaž, Aleksandar Bogojević et al. · 2015 · Computer Physics Communications (arXiv:1601.04640 · doi:10.1016/j.cpc.2015.11.014 · 62 citations). Source: > In this paper we present new versions of previously published numerical programs for solving the dipolar Gross-Pitaevskii (GP) equation including the contact interaction in two and three spatial dimensions in imaginary and in real time, yielding both stationary and non-stationary solutions. New versions of programs were developed using CUDA toolkit and can make use of Nvidia GPU devices. The algorithm used is the same split-step semi-implicit Crank-Nicolson method as in the previous version (R. Kishor Kumar et al., Comput. Phys. Commun. 195, 117 (2015)), which is here implemented as a series o… - **[A new finite element formulation for viscoelastic flows: Circumventing simultaneously the LBB condition and the high-Weissenberg number problem](https://space-kitty.com/papers/doi:10.1016/j.jnnfm.2019.04.003)**. Stylianos Varchanis, Alexandros Syrakos, Yannis Dimakopoulos et al. · 2019 · Journal of Non-Newtonian Fluid Mechanics (doi:10.1016/j.jnnfm.2019.04.003 · 59 citations). Source: - **[OpenMP, OpenMP/MPI, and CUDA/MPI C programs for solving the time-dependent dipolar Gross–Pitaevskii equation](https://space-kitty.com/papers/arxiv:1610.05329)**. Vladimir Lončar, Luis E. Young-S., Srdjan Škrbić et al. · 2016 · Computer Physics Communications (arXiv:1610.05329 · doi:10.1016/j.cpc.2016.07.029 · 59 citations). Source: > We present new versions of the previously published C and CUDA programs for solving the dipolar Gross-Pitaevskii equation in one, two, and three spatial dimensions, which calculate stationary and non-stationary solutions by propagation in imaginary or real time. Presented programs are improved and parallelized versions of previous programs, divided into three packages according to the type of parallelization. First package contains improved and threaded version of sequential C programs using OpenMP. Second package additionally parallelizes three-dimensional variants of the OpenMP programs usin… - **[Modelling of fully-coupled CO2 diffusion and adsorption-induced coal matrix swelling](https://space-kitty.com/papers/doi:10.1016/j.fuel.2019.116486)**. K.H.S.M. Sampath, M.S.A. Perera, Stephan Konrad Matthai et al. · 2019 · Fuel (doi:10.1016/j.fuel.2019.116486 · 57 citations). Source: - **[A Survey of Shortest-Path Algorithms](https://space-kitty.com/papers/arxiv:1705.02044)**. Amgad Madkour, Walid G. Aref, Faizan Ur Rehman et al. · 2017 (arXiv:1705.02044 · 58 citations). Source: > A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of shortest-path algorithms based on a taxonomy that is introduced in the paper. One dimension of this taxonomy is the various flavors of the shortest-path problem. There is no one general algorithm that is capable of solving all variants of the shortest-path problem due to the space and time complexities associated with each algorithm. Other important dimension… - **[Improved Distributed Algorithms for Exact Shortest Paths](https://space-kitty.com/papers/arxiv:1712.09121)**. Mohsen Ghaffari, Jason Li · 2017 · ACM Symposium on Theory of Computing (STOC) (arXiv:1712.09121 · doi:10.1145/3188745.3188948 · 54 citations). Source: > Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm of Becker et al. \[DISC'17\] which deterministically computes $(1+o(1))$-approximate shortest paths in $\\tilde O(D+\\sqrt n)$ time, where $D$ is the hop-diameter of the graph. Up to logarithmic factors, this time complexity is optimal, matching the lower bound of Elkin \[STOC'04\]. The question of exact shortest paths however saw no algorithmic progress for decad… - **[Almost-Linear Time Algorithms for Incremental Graphs: Cycle Detection, SCCs, $s$-$t$ Shortest Path, and Minimum-Cost Flow](https://space-kitty.com/papers/arxiv:2311.18295)**. Li Chen, Rasmus Kyng, Yang P. Liu et al. · 2023 · ACM Symposium on Theory of Computing (STOC) (arXiv:2311.18295 · doi:10.1145/3618260.3649745 · 12 citations). Source: > We give the first almost-linear time algorithms for several problems in incremental graphs including cycle detection, strongly connected component maintenance, $s$-$t$ shortest path, maximum flow, and minimum-cost flow. To solve these problems, we give a deterministic data structure that returns a $m^{o(1)}$-approximate minimum-ratio cycle in fully dynamic graphs in amortized $m^{o(1)}$ time per update. Combining this with the interior point method framework of Brand-Liu-Sidford (STOC 2023) gives the first almost-linear time algorithm for deciding the first update in an incremental graph after… - **[Non‐linear quickflow response as indicators of runoff generation mechanisms](https://space-kitty.com/papers/doi:10.1002/hyp.13780)**. Charles I. Scaife, Nitin K. Singh, R. E. Emanuel et al. · 2020 · Hydrological Processes (doi:10.1002/hyp.13780 · 48 citations). Source: - **[Experimental investigation of frost formation on a parallel flow evaporator](https://space-kitty.com/papers/doi:10.1016/j.apenergy.2010.11.006)**. Jianghong Wu, Guang Ouyang, Puxiu Hou et al. · 2010 · Applied Energy (doi:10.1016/j.apenergy.2010.11.006 · 53 citations). Source: - **[Maximum Flow and Minimum-Cost Flow in Almost-Linear Time](https://space-kitty.com/papers/arxiv:2203.00671)**. Li Chen, Rasmus Kyng, Yang P. Liu et al. · 2022 (arXiv:2203.00671 · 12 citations). Source: > We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with $m$ edges and polynomially bounded integral demands, costs, and capacities in $m^{1+o(1)}$ time. Our algorithm builds the flow through a sequence of $m^{1+o(1)}$ approximate undirected minimum-ratio cycles, each of which is computed and processed in amortized $m^{o(1)}$ time using a new dynamic graph data structure. Our framework extends to algorithms running in $m^{1+o(1)}$ time for computing flows that minimize general edge-separable convex functions to high accuracy. This gives almost-linea… ## Newest - **[Asymptotic Rank of Complete Graph Tensors](https://space-kitty.com/papers/arxiv:2610.34273)**. Huanyi Zhou · 2026 (arXiv:2610.34273). Source: - **[Bicriteria Approximate Navigable Graphs in General Metrics](https://space-kitty.com/papers/arxiv:2610.34302)**. Hongyi Chen, Tianyi Zhang · 2026 (arXiv:2610.34302). Source: - **[Combinatorial Minimum Cost Flow in Almost-Linear Time on Dense Graphs](https://space-kitty.com/papers/arxiv:2610.32556)**. Bernhard Haeupler, Yonggang Jiang, Thatchaphol Saranurak · 2026 (arXiv:2610.32556). Source: - **[Compressed Boolean Matrix Multiplication using Bicliques](https://space-kitty.com/papers/arxiv:2610.32836)**. Nicolás Araya, José Zagal, Cecilia Hernández et al. · 2026 (arXiv:2610.32836). Source: - **[Multiplying matrices via polynomials: exposition and barriers](https://space-kitty.com/papers/arxiv:2610.30054)**. Alimzhan Amanov, Maxim van den Berg, Jeroen Zuiddam · 2026 (arXiv:2610.30054). Source: - **[Polynomial pathwidth for graphs vertex-coverable by few shortest paths and algorithms for quasi-shortest path covers](https://space-kitty.com/papers/arxiv:2610.30458)**. Li-Hsuan Chen, Florent Foucaud, Ling-Ju Hung et al. · 2026 (arXiv:2610.30458). Source: - **[A 55-Addition Rank-23 Scheme for $3\\times3$ Matrix Multiplication via Exact Two-Sided Minimization](https://space-kitty.com/papers/arxiv:2610.27451)**. Greg Sidebottom · 2026 (arXiv:2610.27451). Source: - **[Improved Approximation and Hardness Results for the Monitoring Edge-Geodetic Set Problem](https://space-kitty.com/papers/arxiv:2610.27935)**. Davide Bilò, Giordano Colli, Stefano Leucci · 2026 (arXiv:2610.27935). Source: - **[Dynamic Distances Without Matrix Inverse](https://space-kitty.com/papers/arxiv:2610.28573)**. Jan van den Brand, Adam Karczmarz, Aryan Patel · 2026 (arXiv:2610.28573). Source: - **[Matrix Multiplication from Polynomial Packings: A Constructive and Elementary Proof of $ω\\le9/4$](https://space-kitty.com/papers/arxiv:2610.28627)**. Rafael Pass · 2026 (arXiv:2610.28627). 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