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## An improved optimization algorithm of ads’ allocation in sponsored search and the results of experiments

This paper describes a modified version of an algorithm suggested earlier by the authors for optimizing of ads allocation in sponsored search on the main page of search results in response to user search queries to a web search engine. It is demonstrated that the modification of the algorithm reduces appreciably the searching procedure and the algorithm complexity. And finally, the new algorithm undergoes experimental testing on real data sets provided by Yandex. © 2015, Pleiades Publishing, Ltd.

This book constitutes the proceedings of the 13th International Computer Science Symposium in Russia, CSR 2018, held in Moscow, Russia, in May 2018.

The 24 full papers presented together with 7 invited lectures were carefully reviewed and selected from 42 submissions. The papers cover a wide range of topics such as algorithms and data structures; combinatorial optimization; constraint solving; computational complexity; cryptography; combinatorics in computer science; formal languages and automata; algorithms for concurrent and distributed systems; networks; and proof theory and applications of logic to computer science.

M. Rabin's principle asserts that the depth of any algebraic decision tree, recognizing a closed orthant in scRn, is no less than n. Using the techniques of Newton polyhedra, we give the shortest possible proof of this fact, extending it to arbitrary collections of open or closed orthants, and apply it to trees distinguishing real polynomials having at least l real roots.

We investigate regular realizability (RR) problems, which are the prob- lems of verifying whether intersection of a regular language – the input of the problem – and fixed language called filter is non-empty. In this pa- per we focus on the case of context-free filters. Algorithmic complexity of the RR problem is a very coarse measure of context-free languages com- plexity. This characteristic is compatible with rational dominance. We present examples of P-complete RR problems as well as examples of RR problems in the class NL. Also we discuss RR problems with context- free filters that might have intermediate complexity. Possible candidates are the languages with polynomially bounded rational indices.

The task of complete complexity dichotomy is to clearly distinguish between easy and hard cases of a given problem on a family of subproblems. We consider this task for some optimization problems restricted to certain classes of graphs closed under deletion of vertices. A concept in the solution process is based on revealing the so-called “critical” graph classes, which play an important role in the complexity analysis for the family. Recent progress in studying such classes is presented in the article.

Boolean games are an expressive and natural formalism through which to investigate problems of strategic interaction in multiagent systems. Although they have been widely studied, almost all previous work on Nash equilibria in Boolean games has focused on the restricted setting of pure strategies. This is a shortcoming as finite games are guaranteed to have at least one equilibrium in mixed strategies, but many simple games fail to have pure strategy equilibria at all. We address this by showing that a natural decision problem about mixed equilibria: determining whether a Boolean game has a mixed strategy equilibrium that guarantees every player a given payoff, is NEXP-hard. Accordingly, the epsilon variety of the problem is NEXP-complete. The proof can be adapted to show coNEXP-hardness of a similar question: whether all Nash equilibria of a Boolean game guarantee every player at least the given payoff.

This book constitutes the refereed proceedings of the 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012, held in Helsinki, Finalnd, in July 2012. The 33 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 60 submissions. The papers address issues of searching and matching strings and more complicated patterns such as trees, regular expressions, graphs, point sets, and arrays. The goal is to derive non-trivial combinatorial properties of such structures and to exploit these properties in order to either achieve superior performance for the corresponding computational problems or pinpoint conditions under which searches cannot be performed efficiently. The meeting also deals with problems in computational biology, data compression and data mining, coding, information retrieval, natural language processing, and pattern recognition.

We study the following computational problem: for which values of k, the majority of n bits MAJn can be computed with a depth two formula whose each gate computes a majority function of at most k bits? The corresponding computational model is denoted by MAJk o MAJk. We observe that the minimum value of k for which there exists a MAJk o MAJk circuit that has high correlation with the majority of n bits is equal to Θ(n1/2). We then show that for a randomized MAJk o MAJk circuit computing the majority of n input bits with high probability for every input, the minimum value of k is equal to n2/3+o(1). We show a worst case lower bound: if a MAJk o MAJk circuit computes the majority of n bits correctly on all inputs, then k ≥ n13/19+o(1). This lower bound exceeds the optimal value for randomized circuits and thus is unreachable for pure randomized techniques. For depth 3 circuits we show that a circuit with k = O(n2/3) can compute MAJn correctly on all inputs.

This book constitutes the refereed proceedings of the 44th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2018, held in Krems, Austria, in January/February 2018. The 48 papers presented in this volume were carefully reviewed and selected from 97 submissions. They were organized in topical sections named: foundations of computer science; software engineering: advances methods, applications, and tools; data, information and knowledge engineering; network science and parameterized complexity; model-based software engineering; computational models and complexity; software quality assurance and transformation; graph structure and computation; business processes, protocols, and mobile networks; mobile robots and server systems; automata, complexity, completeness; recognition and generation; optimization, probabilistic analysis, and sorting; filters, configurations, and picture encoding; machine learning; text searching algorithms; and data model engineering.

We consider the coloring problem for hereditary graph classes, i.e. classes of simple unlabeled graphs closed under deletion of vertices. For the family of the hereditary classes of graphs defined by forbidden induced subgraphs with at most four vertices, there are three classes with an open complexity of the problem. For the problem and the open three cases, we present approximation polynomial-time algorithms with performance guarantees.