信息处理和管理(IPM)在计算机与信息科学的交叉点上发布了有关领域,包括但不限于商业、市场营销、广告、社交计算和信息技术等领域的理论、方法或应用的前沿研究。该杂志的目的是通过为及时传播高级和热门问题提供有效的论坛,从而在计算机与信息科学的交叉点上增进研究人员和从业人员的利益。该期刊对原始研究文章、研究调查文章、研究方法文章以及涉及研究关键应用的文章特别感兴趣。官网地址:http://dblp.uni-trier.de/db/journals/ipm/

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We present an $\tilde O(m+n^{1.5})$-time randomized algorithm for maximum cardinality bipartite matching and related problems (e.g. transshipment, negative-weight shortest paths, and optimal transport) on $m$-edge, $n$-node graphs. For maximum cardinality bipartite matching on moderately dense graphs, i.e. $m = \Omega(n^{1.5})$, our algorithm runs in time nearly linear in the input size and constitutes the first improvement over the classic $O(m\sqrt{n})$-time [Dinic 1970; Hopcroft-Karp 1971; Karzanov 1973] and $\tilde O(n^\omega)$-time algorithms [Ibarra-Moran 1981; Mucha-Sankowski 2004] (where currently $\omega\approx 2.373$). On sparser graphs, i.e. when $m = n^{9/8 + \delta}$ for any constant $\delta>0$, our result improves upon the recent advances of [Madry 2013] and [Liu-Sidford 2020b, 2020a] which achieve an $\tilde O(m^{4/3+o(1)})$ runtime. We obtain these results by combining and advancing recent lines of research in interior point methods (IPMs) and dynamic graph algorithms. First, we simplify and improve the IPM of [v.d.Brand-Lee-Sidford-Song 2020], providing a general primal-dual IPM framework and new sampling-based techniques for handling infeasibility induced by approximate linear system solvers. Second, we provide a simple sublinear-time algorithm for detecting and sampling high-energy edges in electric flows on expanders and show that when combined with recent advances in dynamic expander decompositions, this yields efficient data structures for maintaining the iterates of both [v.d.Brand et al.] and our new IPMs. Combining this general machinery yields a simpler $\tilde O(n \sqrt{m})$ time algorithm for matching based on the logarithmic barrier function, and our state-of-the-art $\tilde O(m+n^{1.5})$ time algorithm for matching based on the [Lee-Sidford 2014] barrier (as regularized in [v.d.Brand et al.]).

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We present an $\tilde O(m+n^{1.5})$-time randomized algorithm for maximum cardinality bipartite matching and related problems (e.g. transshipment, negative-weight shortest paths, and optimal transport) on $m$-edge, $n$-node graphs. For maximum cardinality bipartite matching on moderately dense graphs, i.e. $m = \Omega(n^{1.5})$, our algorithm runs in time nearly linear in the input size and constitutes the first improvement over the classic $O(m\sqrt{n})$-time [Dinic 1970; Hopcroft-Karp 1971; Karzanov 1973] and $\tilde O(n^\omega)$-time algorithms [Ibarra-Moran 1981; Mucha-Sankowski 2004] (where currently $\omega\approx 2.373$). On sparser graphs, i.e. when $m = n^{9/8 + \delta}$ for any constant $\delta>0$, our result improves upon the recent advances of [Madry 2013] and [Liu-Sidford 2020b, 2020a] which achieve an $\tilde O(m^{4/3+o(1)})$ runtime. We obtain these results by combining and advancing recent lines of research in interior point methods (IPMs) and dynamic graph algorithms. First, we simplify and improve the IPM of [v.d.Brand-Lee-Sidford-Song 2020], providing a general primal-dual IPM framework and new sampling-based techniques for handling infeasibility induced by approximate linear system solvers. Second, we provide a simple sublinear-time algorithm for detecting and sampling high-energy edges in electric flows on expanders and show that when combined with recent advances in dynamic expander decompositions, this yields efficient data structures for maintaining the iterates of both [v.d.Brand et al.] and our new IPMs. Combining this general machinery yields a simpler $\tilde O(n \sqrt{m})$ time algorithm for matching based on the logarithmic barrier function, and our state-of-the-art $\tilde O(m+n^{1.5})$ time algorithm for matching based on the [Lee-Sidford 2014] barrier (as regularized in [v.d.Brand et al.]).

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