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## LHCb trigger streams optimization

The LHCb experiment stores around 1011 collision events per year. A typical physics analysis deals with a final sample of up to 107 events. Event preselection algorithms (lines) are used for data reduction. Since the data are stored in a format that requires sequential access, the lines are grouped into several output file streams, in order to increase the efficiency of user analysis jobs that read these data. The scheme efficiency heavily depends on the stream composition. By putting similar lines together and balancing the stream sizes it is possible to reduce the overhead. We present a method for finding an optimal stream composition. The method is applied to a part of the LHCb data (Turbo stream) on the stage where it is prepared for user physics analysis. This results in an expected improvement of 15% in the speed of user analysis jobs, and will be applied on data to be recorded in 2017.

This book constitutes the proceedings of the 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016, held in Vladivostok, Russia, in September 2016.

The 39 full papers presented in this volume were carefully reviewed and selected from 181 submissions. They were organized in topical sections named: discrete optimization; scheduling problems; facility location; mathematical programming; mathematical economics and games; applications of operational research; and short communications.

This paper represents our solution for the problem of movement organization based on timetable optimization on the problematic part of railway system, i.e. single-track line. The approximate solution of this problem was founded on the heuristic method. The method gives the exact results in the case of limited amount of parameters and also can be used in the case with huge number of parameters due to reasonable computational time.

In this paper, we consider some scheduling problems on a single machine, where weighted or unweighted total tardiness has to be maximized in contrast to usual minimization problems. These problems are theoretically important and have also practical interpretations. For the weighted tardiness maximization problem, we present an NP-hardness proof and a pseudo-polynomial solution algorithm. For the unweighted total tardiness maximization problem with release dates, NP-hardness is proven. Complexity results for some other classical objective functions (e.g., the number of tardy jobs, total completion time) and various additional constraints (e.g., deadlines, weights and/or release dates of jobs may be given) are presented as well.

In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. A pseudo-polynomial time solution algorithm is proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted number of tardy jobs on a single machine. The latter algorithm improves the complexity of an existing pseudo-polynomial algorithm by Lawler. Computational results are presented for both special cases considered.

Global Equilibrium Search (GES) is a meta-heuristic framework that shares similar ideas with the simulated annealing method. GES accumulates a compact set of information about the search space to generate promising initial solutions for the techniques that require a starting solution, such as the simple local search method. GES has been successful for many classic discrete optimization problems: the unconstrained quadratic programming problem, the maximum satisfiability problem, the max-cut problem, the multidimensional knapsack problem and the job-shop scheduling problem. GES provides state-of-the-art performance on all of these domains when compared to the current best known algorithms from the literature. GES algorithm can be naturally extended for parallel computing as it performs search simultaneously in distinct areas of the solution space. In this talk, we provide an overview of Global Equilibrium Search and discuss some successful applications.

A railway connection of two stations by a single railway track is usually found on branch lines of railway network and is very common in various manufacturing supply chains. Our paper isДля книг на иностранных языках concerned with a scheduling problem for two stations with a single railway track with one siding. On single-track railway sidings or passing loops are used to increase the capacity of the line. In our paper we developed exact optimization algorithm by analysing the structure of optimal schedule for the proposed model. The algorithm produces a schedule that completes all transportations between two stations at minimal time. We present algorithm to construct an optimal schedule in O(1) operations. Optimal schedule analyse allows the development of exact optimization algorithms with other models and objective functions, i.e. results can be generalized and used in future work for a number of regular objective functions, commonly used in scheduling.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.

It is well-known that the class of sets that can be computed by polynomial size circuits is equal to the class of sets that are polynomial time reducible to a sparse set. It is widely believed, but unfortunately up to now unproven, that there are sets in EXPNP, or even in EXP that are not computable by polynomial size circuits and hence are not reducible to a sparse set. In this paper we study this question in a more restricted setting: what is the computational complexity of sparse sets that are *selfreducible*? It follows from earlier work of Lozano and Torán (in: Mathematical systems theory, 1991) that EXPNP does not have sparse selfreducible hard sets. We define a natural version of selfreduction, tree-selfreducibility, and show that NEXP does not have sparse tree-selfreducible hard sets. We also construct an oracle relative to which all of EXP is reducible to a sparse tree-selfreducible set. These lower bounds are corollaries of more general results about the computational complexity of sparse sets that are selfreducible, and can be interpreted as super-polynomial circuit lower bounds for NEXP.