DOI: 10.3217/jucs-025-02-0098

Authors: Guilherme Henrique Santos Miranda, Carla Lintzmayer, Zanoni Dias

Abstract: For estimating the evolutionary distance between genomes of two different organisms, many sorting permutation problems have emerged. A well accepted way to do this is considering the smallest sequence of rearrangement events { mutations which affect large portions of the genomes { that transform one genome into the other. In these problems, both genomes are represented as permutations of integer numbers, but one of them can be represented as the identity permutation, so that the problem is reduced to sort a permutation. Moreover, rearrangement models define which type of operations (rearrangement events) can be applied over a permutation in order to modify it. Reversals, which are operations that revert a genome segment, and transpositions, which are operations that swap two adjacent genome segments, are two of the most studied types of rearrangements in the literature. In this paper, we consider rearrangement models that allow reversals, transpositions, and both operations together. Since there exist evidences that large mutations rarely occur, we add a restriction with biological relevance: any operation can affect at most λ elements of a permutation. For this variation of sorting permutation problem, we present approximation algorithms with approximation factors based on the size of the permutation and/or on λ, for both signed and unsigned permutations (which represent known and unknown gene orientations, respectively).

]]>DOI: 10.3217/jucs-023-09-0868

Authors: Andre Oliveira, Ulisses Dias, Zanoni Dias

Abstract: Reversals and transpositions are two classic genome rearrangement operations. Reversals occur when a chromosome breaks at two locations called breakpoints and the DNA between the breakpoints is reversed. Transpositions occur when two adjacent blocks of elements exchange position. This paper presents a polynomial-time approximation algorithm for the Sorting by Reversals and Transpositions Problem. Our algorithm applies to both signed and unsigned versions of the problem, and it treats both cases in a unified manner. We prove an approximation factor of 2 for signed permutations and 2k for the unsigned case, where k is the approximation factor of the algorithm used for cycle decomposition, but in our practical experiments our algorithm found results with approximation ratio better than 1.5 in more than 99% of the signed permutations and better than 1.8 in more than 97% of the unsigned permutations. Our analysis also shows that our algorithm outperforms any other approach known to date.

]]>DOI: 10.3217/jucs-020-13-1855

Authors: Ming Yang, Bo Liu, Wei Wang, Junzhou Luo, Xiaojun Shen

Abstract: By exploiting multi-radio multi-channel technology, wireless mesh networks can effectively provide wireless broadband access to the Internet for mobile users. Due to the limited number of orthogonal channels, overlapping channel assignment is one of the main factors that greatly affect the network capacity. However, current results in this area are not so satisfying. In this paper, we first propose a model for measuring achieved network capacity in MR-WMNs. Then we prove that finding an optimal overlapping channel assignment in a given MR-WMN with odd number of channels, is equivalent to finding an optimal assignment by only using its orthogonal channels. This theory allows us to use fewer channels to solve complicated channel assignment problems. Third, we prove that in 802.11b/g MR-WMN the simplified optimization problem is a Max-3-Cut problem. Although this problem is NP-hard, it has an efficient approximation algorithm that achieves approximation ratio of 1.19616 probabilistically by using the algorithm for Max-Cut whose approximation ratio is 1.1383 probabilistically. Based on the algorithm for Max-Cut, this paper proposes Max-Cut based channel assignment (MCCA) which uses a heuristic method to adjust the result produced by the Max-Cut algorithm to achieve an even better result. Finally, we perform extensive simulations to compare the MCCA with a state-of-the-art Tabu-Search based algorithm. The results show that the Max-Cut based overlapping channel assignment algorithm effectively and efficiently improves on the network capacity compared with existing algorithms.

]]>DOI: 10.3217/jucs-020-09-1259

Authors: Gustavo Galvão, Zanoni Dias

Abstract: We study the problem of sorting by transpositions, which consists in computing the minimum number of transpositions required to sort a permutation. This problem is NP-hard and the best approximation algorithms for solving it are based on a standard tool for attacking problems of this kind, the cycle graph. In an attempt to bypass it, some researches posed alternative approaches. In this paper, we address three algorithms yielded by such approaches: a 2.25-approximation algorithm based on breakpoint diagrams, a 3-approximation algorithm based on permutation codes, and a heuristic based on longest increasing subsequences. Regarding the 2.25-approximation algorithm, we show that previous experimental data on its approximation ratio are incorrect. Regarding the 3-approximation algorithm, we close a missing gap on the proof of its approximation ratio and we show a way to run it in O(n log n) time. Regarding the heuristic, we propose a minor adaptation that allow us to prove an approximation bound of 3. We present experimental data obtained by running these algorithms for all permutations with up to 13 elements and by running these algorithms and the best known algorithms based on the cycle graph for large permutations. The data indicate that the 2.25-approximation algorithm is the best of the algorithms based on alternative approaches and that it is the only one comparable to the algorithms based on the cycle graph.

]]>DOI: 10.3217/jucs-018-04-0577

Authors: Anna Zygmunt, Piotr Bródka, Przemysław Kazienko, Jarosław Koźlak

Abstract: Identifying key persons active in social groups in the blogosphere is performed by means of social network analysis. Two main independent approaches are considered in the paper: (i) discovery of the most important individuals in persistent social communities and (ii) regular centrality measures applied either to social groups or the entire network. A new method for separating of groups stable over time, fulfilling given conditions of activity level of their members is proposed. Furthermore, a new concept for extracting user roles and key persons in such groups is also presented. This new approach was compared to the typical clustering method and the structural node position measure applied to rank users. The experimental studies have been carried out on real two-year blogosphere data.

]]>