Capacitated max-Batching with Interval Graph Compatibilities

We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the cost of a clique is the maximum weight of any interval in the clique. This natural graph problem can be interpreted as a batch scheduling problem. Solving an open question from [7, 4, 5], we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we give a PTAS based on a novel dynamic programming technique for this case.

Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP

2-Opt is probably the most basic local search heuristic for the TSP. This heuristic achieves amazingly good results on “real world” Euclidean instances both with respect to running time and approximation ratio. There are numerous experimental studies on the performance of 2-Opt. However, the theoretical knowledge about this heuristic is still very limited. Not even its worst case running time on 2-dimensional Euclidean instances was known so far. We clarify this issue by presenting, for every p∈N , a family of L p instances on which 2-Opt can take an exponential number of steps. Previous probabilistic analyses were restricted to instances in which n points are placed uniformly at random in the unit square [0,1]2, where it was shown that the expected number of steps is bounded by O~(n10) for Euclidean instances. We consider a more advanced model of probabilistic instances in which the points can be placed independently according to general distributions on [0,1] d , for an arbitrary d≥2. In particular, we allow different distributions for different points. We study the expected number of local improvements in terms of the number n of points and the maximal density ϕ of the probability distributions. We show an upper bound on the expected length of any 2-Opt improvement path of O~(n4+1/3⋅ϕ8/3) . When starting with an initial tour computed by an insertion heuristic, the upper bound on the expected number of steps improves even to O~(n4+1/3−1/d⋅ϕ8/3) . If the distances are measured according to the Manhattan metric, then the expected number of steps is bounded by O~(n4−1/d⋅ϕ) . In addition, we prove an upper bound of O(ϕ√d) on the expected approximation factor with respect to all L p metrics. Let us remark that our probabilistic analysis covers as special cases the uniform input model with ϕ=1 and a smoothed analysis with Gaussian perturbations of standard deviation σ with ϕ∼1/σ d

Bounded version vectors

Version vectors play a central role in update tracking under optimistic distributed systems, allowing the detection of obsolete or inconsistent versions of replicated data. Version vectors do not have a bounded representation; they are based on integer counters that grow indefinitely as updates occur. Existing approaches to this problem are scarce; the mechanisms proposed are either unbounded or operate only under specific settings. This paper examines version vectors as a mechanism for data causality tracking and clarifies their role with respect to vector clocks. Then, it introduces bounded stamps and proves them to be a correct alternative to integer counters in version vectors. The resulting mechanism, bounded version vectors, represents the first bounded solution to data causality tracking between replicas subject to local updates and pairwise symmetrical synchronization.FCT project POSI/ICHS/44304/2002, FCT under grant BSAB/390/2003

An introduction to description logics and query rewriting

This chapter gives an overview of the description logics underlying the OWL 2 Web Ontology Language and its three tractable profiles, OWL 2 RL, OWL 2 EL and OWL 2 QL. We consider the syntax and semantics of these description logics as well as main reasoning tasks and their computational complexity. We also discuss the semantical foundations for fist-order and datalog rewritings of conjunctive queries over knowledge bases given in the OWL2 profiles, and outline the architecture of the ontology-based data access system Ontop

An Iterated Local Search Approach for Finding Provably Good Solutions for Very Large TSP Instances

Abstract. Meta-heuristics usually lack any kind of performance guar-antee and therefore one cannot be certain whether the resulting solutions are (near) optimum solutions or not without relying on additional algo-rithms for providing lower bounds (in case of minimization). In this paper, we present a highly effective hybrid evolutionary local search algorithm based on the iterated Lin-Kernighan heuristic combined with a lower bound heuristic utilizing 1-trees. Since both upper and lower bounds are improved over time, the gap between the two bounds is minimized by means of effective heuristics. In experiments, we show that the proposed approach is capable of finding short tours with a gap of 0.8 % or less for TSP instances up to 10 million cities. Hence, to the best of our knowledge, we present the first evolutionary algorithm and meta-heuristic in general that delivers provably good solutions and is highly scalable with the problem size. We show that our approach outperforms all existing heuristics for very large TSP instances.

Global Carbon Budget 2018

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere – the “global carbon budget” – is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and methodology to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFF) are based on energy statistics and cement production data, while emissions from land use and land-use change (ELUC), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) and terrestrial CO2 sink (SLAND) are estimated with global process models constrained by observations. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the last decade available (2008–2017), EFF was 9.4±0.5 GtC yr−1, ELUC 1.5±0.7 GtC yr−1, GATM 4.7±0.02 GtC yr−1, SOCEAN 2.4±0.5 GtC yr−1, and SLAND 3.2±0.8 GtC yr−1, with a budget imbalance BIM of 0.5 GtC yr−1 indicating overestimated emissions and/or underestimated sinks. For the year 2017 alone, the growth in EFF was about 1.6 % and emissions increased to 9.9±0.5 GtC yr−1. Also for 2017, ELUC was 1.4±0.7 GtC yr−1, GATM was 4.6±0.2 GtC yr−1, SOCEAN was 2.5±0.5 GtC yr−1, and SLAND was 3.8±0.8 GtC yr−1, with a BIM of 0.3 GtC. The global atmospheric CO2 concentration reached 405.0±0.1 ppm averaged over 2017. For 2018, preliminary data for the first 6–9 months indicate a renewed growth in EFF of +2.7 % (range of 1.8 % to 3.7 %) based on national emission projections for China, the US, the EU, and India and projections of gross domestic product corrected for recent changes in the carbon intensity of the economy for the rest of the world. The analysis presented here shows that the mean and trend in the five components of the global carbon budget are consistently estimated over the period of 1959–2017, but discrepancies of up to 1 GtC yr−1 persist for the representation of semi-decadal variability in CO2 fluxes. A detailed comparison among individual estimates and the introduction of a broad range of observations show (1) no consensus in the mean and trend in land-use change emissions, (2) a persistent low agreement among the different methods on the magnitude of the land CO2 flux in the northern extra-tropics, and (3) an apparent underestimation of the CO2 variability by ocean models, originating outside the tropics. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding the global carbon cycle compared with previous publications of this data set (Le Quéré et al., 2018, 2016, 2015a, b, 2014, 2013). All results presented here can be downloaded from https://doi.org/10.18160/GCP-2018

Search for the associated production of the Higgs boson with a top-quark pair

A search for the standard model Higgs boson produced in association with a top-quark pair t t ¯ H (tt¯H) is presented, using data samples corresponding to integrated luminosities of up to 5.1 fb −1 and 19.7 fb −1 collected in pp collisions at center-of-mass energies of 7 TeV and 8 TeV respectively. The search is based on the following signatures of the Higgs boson decay: H → hadrons, H → photons, and H → leptons. The results are characterized by an observed t t ¯ H tt¯H signal strength relative to the standard model cross section, μ = σ/σ SM ,under the assumption that the Higgs boson decays as expected in the standard model. The best fit value is μ = 2.8 ± 1.0 for a Higgs boson mass of 125.6 GeV