Breaking the nn-Pass Barrier: A Streaming Algorithm for Maximum Weight Bipartite Matching

Given a weighted bipartite graph with $n$ vertices and $m$ edges, the \emph{maximum weight bipartite matching} problem is to find a set of vertex-disjoint edges with the maximum weight. This classic problem has been extensively studied for over a century. In this paper, we present a new streaming algorithm for the maximum weight bipartite matching problem that uses $\widetilde{O}(n)$ space and $\widetilde{O}(\sqrt{m})$ passes, which breaks the $n$-pass barrier. All the previous streaming algorithms either require $\Omega(n \log n)$ passes or only find an approximate solution. Our streaming algorithm constructs a subgraph with $n$ edges of the input graph in $\widetilde{O}(\sqrt{m})$ passes, such that the subgraph admits the optimal matching with good probability. Our method combines various ideas from different fields, most notably the construction of \emph{space-efficient} interior point method (IPM), SDD system solvers, the isolation lemma, and LP duality. To the best of our knowledge, this is the first work that implements the SDD solvers and IPMs in the streaming model in $\widetilde{O}(n)$ spaces for graph matrices; previous IPM algorithms only focus on optimizing the running time, regardless of the space usage

Interleukin-22 signaling attenuates necrotizing enterocolitis by promoting epithelial cell regeneration

Necrotizing enterocolitis (NEC) is a deadly intestinal inflammatory disorder that primarily affects premature infants and lacks adequate therapeutics. Interleukin (IL)-22 plays a critical role in gut barrier maintenance, promoting epithelial regeneration, and controlling intestinal inflammation in adult animal models. However, the importance of IL-22 signaling in neonates during NEC remains unknown. We investigated the role of IL-22 in the neonatal intestine under homeostatic and inflammatory conditions by using a mouse model of NEC. Our data reveal tha

Search for CP violation in D+→ϕπ+ and D+s→K0Sπ+ decays

A search for CP violation in D + → ϕπ + decays is performed using data collected in 2011 by the LHCb experiment corresponding to an integrated luminosity of 1.0 fb−1 at a centre of mass energy of 7 TeV. The CP -violating asymmetry is measured to be (−0.04 ± 0.14 ± 0.14)% for candidates with K − K + mass within 20 MeV/c 2 of the ϕ meson mass. A search for a CP -violating asymmetry that varies across the ϕ mass region of the D + → K − K + π + Dalitz plot is also performed, and no evidence for CP violation is found. In addition, the CP asymmetry in the D+s→K0Sπ+ decay is measured to be (0.61 ± 0.83 ± 0.14)%

Observation of two new Ξb−\Xi_b^- baryon resonances

Two structures are observed close to the kinematic threshold in the $\Xi_b^0 \pi^-$ mass spectrum in a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb$^{-1}$ recorded by the LHCb experiment. In the quark model, two baryonic resonances with quark content $bds$ are expected in this mass region: the spin-parity $J^P = \frac{1}{2}^+$ and $J^P=\frac{3}{2}^+$ states, denoted $\Xi_b^{\prime -}$ and $\Xi_b^{*-}$. Interpreting the structures as these resonances, we measure the mass differences and the width of the heavier state to be $m(\Xi_b^{\prime -}) - m(\Xi_b^0) - m(\pi^{-}) = 3.653 \pm 0.018 \pm 0.006$ MeV$/c^2$, $m(\Xi_b^{*-}) - m(\Xi_b^0) - m(\pi^{-}) = 23.96 \pm 0.12 \pm 0.06$ MeV$/c^2$, $\Gamma(\Xi_b^{*-}) = 1.65 \pm 0.31 \pm 0.10$ MeV, where the first and second uncertainties are statistical and systematic, respectively. The width of the lighter state is consistent with zero, and we place an upper limit of $\Gamma(\Xi_b^{\prime -}) < 0.08$ MeV at 95% confidence level. Relative production rates of these states are also reported.Comment: 17 pages, 2 figure