Making Three out of Two: Three-Way Online Correlated Selection

Two-way online correlated selection (two-way OCS) is an online algorithm that, at each timestep, takes a pair of elements from the ground set and irrevocably chooses one of the two elements, while ensuring negative correlation in the algorithm\u27s choices. Whilst OCS was initially invented by Fahrbach, Huang, Tao, and Zadimoghaddam to break a natural long-standing barrier in the edge-weighted online bipartite matching problem, it is an interesting technique on its own due to its capability of introducing a powerful algorithmic tool, namely negative correlation, to online algorithms. As such, Fahrbach et al. posed two tantalizing open questions in their paper, one of which was the following: Can we obtain n-way OCS for n > 2, in which the algorithm can be given n > 2 elements to choose from at each timestep? In this paper, we affirmatively answer this open question by presenting a three-way OCS. Our algorithm uses two-way OCS as its building block and is simple to describe; however, as it internally runs two instances of two-way OCS, one of which is fed with the output of the other, the final output probability distribution becomes highly elusive. We tackle this difficulty by approximating the output distribution of OCS by a flat, less correlated function and using it as a safe "surrogate" of the real distribution. Our three-way OCS also yields a 0.5093-competitive algorithm for edge-weighted online matching, demonstrating its usefulness

Constant-Factor Approximation Algorithms for the Parity-Constrained Facility Location Problem

Facility location is a prominent optimization problem that has inspired a large quantity of both theoretical and practical studies in combinatorial optimization. Although the problem has been investigated under various settings reflecting typical structures within the optimization problems of practical interest, little is known on how the problem behaves in conjunction with parity constraints. This shortfall of understanding was rather discouraging when we consider the central role of parity in the field of combinatorics. In this paper, we present the first constant-factor approximation algorithm for the facility location problem with parity constraints. We are given as the input a metric on a set of facilities and clients, the opening cost of each facility, and the parity requirement - odd, even, or unconstrained - of every facility in this problem. The objective is to open a subset of facilities and assign every client to an open facility so as to minimize the sum of the total opening costs and the assignment distances, but subject to the condition that the number of clients assigned to each open facility must have the same parity as its requirement. Although the unconstrained facility location problem as a relaxation for this parity-constrained generalization has unbounded gap, we demonstrate that it yields a structured solution whose parity violation can be corrected at small cost. This correction is prescribed by a T-join on an auxiliary graph constructed by the algorithm. This auxiliary graph does not satisfy the triangle inequality, but we show that a carefully chosen set of shortcutting operations leads to a cheap and sparse T-join. Finally, we bound the correction cost by exhibiting a combinatorial multi-step construction of an upper bound

Improved Learning-Augmented Algorithms for the Multi-Option Ski Rental Problem via Best-Possible Competitive Analysis

In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.Comment: 23 pages, 1 figur

Combined searches for the production of supersymmetric top quark partners in proton-proton collisions at root s=13 TeV

A combination of searches for top squark pair production using proton-proton collision data at a center-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 137 fb(-1) collected by the CMS experiment, is presented. Signatures with at least 2 jets and large missing transverse momentum are categorized into events with 0, 1, or 2 leptons. New results for regions of parameter space where the kinematical properties of top squark pair production and top quark pair production are very similar are presented. Depending on themodel, the combined result excludes a top squarkmass up to 1325 GeV for amassless neutralino, and a neutralinomass up to 700 GeV for a top squarkmass of 1150 GeV. Top squarks with masses from 145 to 295 GeV, for neutralino masses from 0 to 100 GeV, with a mass difference between the top squark and the neutralino in a window of 30 GeV around the mass of the top quark, are excluded for the first time with CMS data. The results of theses searches are also interpreted in an alternative signal model of dark matter production via a spin-0 mediator in association with a top quark pair. Upper limits are set on the cross section for mediator particle masses of up to 420 GeV

Observation of tW production in the single-lepton channel in pp collisions at root s=13 TeV

A measurement of the cross section of the associated production of a single top quark and a W boson in final states with a muon or electron and jets in proton-proton collisions at root s = 13 TeV is presented. The data correspond to an integrated luminosity of 36 fb(-1) collected with the CMS detector at the CERN LHC in 2016. A boosted decision tree is used to separate the tW signal from the dominant t (t) over bar background, whilst the subleading W+jets and multijet backgrounds are constrained using data-based estimates. This result is the first observation of the tW process in final states containing a muon or electron and jets, with a significance exceeding 5 standard deviations. The cross section is determined to be 89 +/- 4 (stat) +/- 12 (syst) pb, consistent with the standard model.Peer reviewe

Measurement of the top quark mass using events with a single reconstructed top quark in pp collisions at root s=13 TeV

Abstract:A measurement of the top quark mass is performed using a data sample en-riched with single top quark events produced in thetchannel. The study is based on proton-proton collision data, corresponding to an integrated luminosity of 35.9 fb−1, recorded at√s= 13TeV by the CMS experiment at the LHC in 2016. Candidate events are selectedby requiring an isolated high-momentum lepton (muon or electron) and exactly two jets,of which one is identified as originating from a bottom quark. Multivariate discriminantsare designed to separate the signal from the background. Optimized thresholds are placedon the discriminant outputs to obtain an event sample with high signal purity. The topquark mass is found to be172.13+0.76−0.77GeV, where the uncertainty includes both the sta-tistical and systematic components, reaching sub-GeV precision for the first time in thisevent topology. The masses of the top quark and antiquark are also determined separatelyusing the lepton charge in the final state, from which the mass ratio and difference aredetermined to be0.9952+0.0079−0.0104and0.83+1.79−1.35GeV, respectively. The results are consistentwithCPTinvariance

Search for a heavy Higgs boson decaying into two lighter Higgs bosons in the tau tau bb final state at 13 TeV

A search for a heavy Higgs boson H decaying into the observed Higgs boson h with a mass of 125 GeV and another Higgs boson h(S) is presented. The h and h(S) bosons are required to decay into a pair of tau leptons and a pair of b quarks, respectively. The search uses a sample of proton-proton collisions collected with the CMS detector at a center-of-mass energy of 13TeV, corresponding to an integrated luminosity of 137 fb(-1). Mass ranges of 240-3000 GeV for m(H) and 60-2800 GeV for m(hS) are explored in the search. No signal has been observed. Model independent 95% confidence level upper limits on the product of the production cross section and the branching fractions of the signal process are set with a sensitivity ranging from 125 fb (for m(H) = 240 GeV) to 2.7 fb (for m(H) = 1000 GeV). These limits are compared to maximally allowed products of the production cross section and the branching fractions of the signal process in the next-to-minimal supersymmetric extension of the standard model.Peer reviewe

Measurements of Higgs boson production cross sections and couplings in the diphoton decay channel at root s=13 TeV

Measurements of Higgs boson production cross sections and couplings in events where the Higgs boson decays into a pair of photons are reported. Events are selected from a sample of proton-proton collisions at root s = 13TeV collected by the CMS detector at the LHC from 2016 to 2018, corresponding to an integrated luminosity of 137 fb(-1). Analysis categories enriched in Higgs boson events produced via gluon fusion, vector boson fusion, vector boson associated production, and production associated with top quarks are constructed. The total Higgs boson signal strength, relative to the standard model (SM) prediction, is measured to be 1.12 +/- 0.09. Other properties of the Higgs boson are measured, including SM signal strength modifiers, production cross sections, and its couplings to other particles. These include the most precise measurements of gluon fusion and vector boson fusion Higgs boson production in several different kinematic regions, the first measurement of Higgs boson production in association with a top quark pair in five regions of the Higgs boson transverse momentum, and an upper limit on the rate of Higgs boson production in association with a single top quark. All results are found to be in agreement with the SM expectations.Peer reviewe