Pub Date : 2024-11-29DOI: 10.1007/s00236-024-00468-6
Zhongzheng Tang, Haoyang Zou, Zhuo Diao
Let H(V, E) be a k-regular connected hypergraph with rank R on n vertices and m edges. A set of vertices (Ssubseteq V) is an independent set if every two vertices in S are not adjacent. The independence number is the maximum cardinality of an independent set, denoted by (alpha (H)). In this paper, we prove the following inequality: (alpha (H)ge frac{m-(k-2)n-1}{R}), and the equality holds if and only if H is a hypertree with R-perfect matching. Based on the proofs, some combinatorial algorithms on the independence number are designed.
{"title":"A sharp lower bound on the independence number of k-regular connected hypergraphs with rank R","authors":"Zhongzheng Tang, Haoyang Zou, Zhuo Diao","doi":"10.1007/s00236-024-00468-6","DOIUrl":"10.1007/s00236-024-00468-6","url":null,"abstract":"<div><p>Let <i>H</i>(<i>V</i>, <i>E</i>) be a <i>k</i>-regular connected hypergraph with rank <i>R</i> on <i>n</i> vertices and <i>m</i> edges. A set of vertices <span>(Ssubseteq V)</span> is an independent set if every two vertices in <i>S</i> are not adjacent. The independence number is the maximum cardinality of an independent set, denoted by <span>(alpha (H))</span>. In this paper, we prove the following inequality: <span>(alpha (H)ge frac{m-(k-2)n-1}{R})</span>, and the equality holds if and only if <i>H</i> is a hypertree with <i>R</i>-perfect matching. Based on the proofs, some combinatorial algorithms on the independence number are designed.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-28DOI: 10.1007/s00236-024-00471-x
Hui Jiang, Jianling Fu, Yuxin Deng, Jun Wu
It is a current trend of sparse architectures employed for superconducting quantum chips, which have the advantage of low coupling and crosstalk properties. Existing qubit mapping algorithms do not take the sparsity of quantum architectures into account. To this end, we propose a qubit mapping method based on binary integer programming, called QMBIP. First, we slice a given quantum circuit by taking into account the sparsity of target architectures. Then, the constraints and the objective function are formulated and rendered to the binary integer programming problem by matrix transformation. The behavior of a (textbf{SWAP}) gate is characterized by an elementary row transformation on the mapping matrix between the physical and logical qubits. To reduce the search space, we introduce path variables and isomorphic pruning, as well as a look-ahead mechanism. Finally, we compare with typical qubit mapping algorithms such as SABRE and SATMAP on the sparse architectures ibmq_sydney, ibmq_manhattan, ibmq_singapore, and a dense architecture ibmq_tokyo. Experiments show that QMBIP effectively maintains the fidelity of the compiled quantum circuits. For example, on ibmq_sydney, the fidelity of the quantum circuits compiled by our approach outperforms SABRE and SATMAP by 53.9% and 46.8%, respectively.
{"title":"A binary integer programming-based method for qubit mapping in sparse architectures","authors":"Hui Jiang, Jianling Fu, Yuxin Deng, Jun Wu","doi":"10.1007/s00236-024-00471-x","DOIUrl":"10.1007/s00236-024-00471-x","url":null,"abstract":"<div><p>It is a current trend of sparse architectures employed for superconducting quantum chips, which have the advantage of low coupling and crosstalk properties. Existing qubit mapping algorithms do not take the sparsity of quantum architectures into account. To this end, we propose a qubit mapping method based on binary integer programming, called QMBIP. First, we slice a given quantum circuit by taking into account the sparsity of target architectures. Then, the constraints and the objective function are formulated and rendered to the binary integer programming problem by matrix transformation. The behavior of a <span>(textbf{SWAP})</span> gate is characterized by an elementary row transformation on the mapping matrix between the physical and logical qubits. To reduce the search space, we introduce path variables and isomorphic pruning, as well as a look-ahead mechanism. Finally, we compare with typical qubit mapping algorithms such as SABRE and SATMAP on the sparse architectures <i>ibmq_sydney</i>, <i>ibmq_manhattan</i>, <i>ibmq_singapore</i>, and a dense architecture <i>ibmq_tokyo</i>. Experiments show that QMBIP effectively maintains the fidelity of the compiled quantum circuits. For example, on <i>ibmq_sydney</i>, the fidelity of the quantum circuits compiled by our approach outperforms SABRE and SATMAP by 53.9% and 46.8%, respectively.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-27DOI: 10.1007/s00236-024-00470-y
Yueguo Luo, Yuzhen Zhao, Wenqin Li, Ping Guo
P systems are distributed, parallel computing models inspired by biology. Tissue-like P systems are an important variant of P systems, where the environment can provide objects for cells. Hence, the environment plays a critical role. Nevertheless, in actual biological tissues, there exists a peculiar biological phenomenon called “homeostasis”; that is, the internal organisms maintain stable, thereby reducing their dependence on external conditions (i.e., the environment). In this work, considering cell separation, we construct a novel variant to simulate the mechanism of biological homeostasis, called homeostasis tissue-like P systems with cell separation. In this variant, the number of object is finite, and certain substance changes occur inside the cells; moreover, an exponential workspace can be obtained with cell separation in feasible time. The computational power of this model is studied by simulating register machines, and the results show that the variant is computationally complete as number computing devices. Furthermore, to explore the computational efficiency of the model, we use the variant to solve a classic (textbf{NP})-complete problem, the SAT problem, obtaining a uniform solution with a rule length of at most 3.
P 系统是受生物学启发的分布式并行计算模型。类组织 P 系统是 P 系统的一个重要变体,其中环境可以为细胞提供对象。因此,环境起着至关重要的作用。然而,在实际的生物组织中,存在一种奇特的生物现象,即 "稳态";也就是说,内部有机体保持稳定,从而减少对外部条件(即环境)的依赖。在这项工作中,考虑到细胞分离,我们构建了一种新的变体来模拟生物平衡机制,称为具有细胞分离的类平衡组织 P 系统。在这一变体中,物体的数量是有限的,细胞内会发生某些物质变化;此外,在可行的时间内,细胞分离可获得指数工作空间。我们通过模拟寄存器对该模型的计算能力进行了研究,结果表明,作为数字计算设备,该变量在计算上是完整的。此外,为了探索该模型的计算效率,我们用该变体求解了一个经典的(textbf{NP})-完全问题--SAT问题,得到了规则长度最多为3的统一解。
{"title":"Homeostasis tissue-like P systems with cell separation","authors":"Yueguo Luo, Yuzhen Zhao, Wenqin Li, Ping Guo","doi":"10.1007/s00236-024-00470-y","DOIUrl":"10.1007/s00236-024-00470-y","url":null,"abstract":"<div><p>P systems are distributed, parallel computing models inspired by biology. Tissue-like P systems are an important variant of P systems, where the environment can provide objects for cells. Hence, the environment plays a critical role. Nevertheless, in actual biological tissues, there exists a peculiar biological phenomenon called “homeostasis”; that is, the internal organisms maintain stable, thereby reducing their dependence on external conditions (i.e., the environment). In this work, considering cell separation, we construct a novel variant to simulate the mechanism of biological homeostasis, called homeostasis tissue-like P systems with cell separation. In this variant, the number of object is finite, and certain substance changes occur inside the cells; moreover, an exponential workspace can be obtained with cell separation in feasible time. The computational power of this model is studied by simulating register machines, and the results show that the variant is computationally complete as number computing devices. Furthermore, to explore the computational efficiency of the model, we use the variant to solve a classic <span>(textbf{NP})</span>-complete problem, the SAT problem, obtaining a uniform solution with a rule length of at most 3.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1007/s00236-024-00469-5
Joydeep Mukherjee, Tamojit Saha
A connected feedback vertex set of a graph is a connected subgraph of the graph whose removal makes the graph cycle free. In this paper, we provide an approximation algorithm for connected feedback vertex set in AT-free graphs. Given an (alpha )-approximate solution for feedback vertex set on 2-connected AT-free graph, our algorithm produces a solution of size (((alpha +0.9091)OPT+6)) for connected feedback vertex set on the same graph. The complexity of our algorithm is (O(f(n)+(m+n))), where the time required to obtain the (alpha )-approximate solution is O(f(n)). Our result leads to the following two observations. The optimal feedback vertex set algorithm for AT-free graphs combined with our result provides an algorithm which produces a solution of size ((1.9091OPT+6)) with running time (O(n^8m^2)) for 2-connected AT-free graphs. The 2-approximation algorithm for feedback vertex set in general graphs along with our result provides an algorithm which produces a solution of size ((2.9091OPT+6)) with running time (O(min{m(log(n)),n^2})). Using the same method we also obtain a (((alpha +1)OPT+6))-approximation for this problem on general AT-free graphs. We note that, the complexity status of this problem is not known.
{"title":"Connected feedback vertex set on AT-free graphs","authors":"Joydeep Mukherjee, Tamojit Saha","doi":"10.1007/s00236-024-00469-5","DOIUrl":"10.1007/s00236-024-00469-5","url":null,"abstract":"<div><p>A connected feedback vertex set of a graph is a connected subgraph of the graph whose removal makes the graph cycle free. In this paper, we provide an approximation algorithm for connected feedback vertex set in AT-free graphs. Given an <span>(alpha )</span>-approximate solution for feedback vertex set on 2-connected AT-free graph, our algorithm produces a solution of size <span>(((alpha +0.9091)OPT+6))</span> for connected feedback vertex set on the same graph. The complexity of our algorithm is <span>(O(f(n)+(m+n)))</span>, where the time required to obtain the <span>(alpha )</span>-approximate solution is <i>O</i>(<i>f</i>(<i>n</i>)). Our result leads to the following two observations. The optimal feedback vertex set algorithm for AT-free graphs combined with our result provides an algorithm which produces a solution of size <span>((1.9091OPT+6))</span> with running time <span>(O(n^8m^2))</span> for 2-connected AT-free graphs. The 2-approximation algorithm for feedback vertex set in general graphs along with our result provides an algorithm which produces a solution of size <span>((2.9091OPT+6))</span> with running time <span>(O(min{m(log(n)),n^2}))</span>. Using the same method we also obtain a <span>(((alpha +1)OPT+6))</span>-approximation for this problem on general AT-free graphs. We note that, the complexity status of this problem is not known.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-21DOI: 10.1007/s00236-024-00467-7
Lucas P. Ramos, Felipe A. Louza, Guilherme P. Telles
DNA technologies have evolved significantly in the past years enabling the sequencing of a large number of genomes in a short time. Nevertheless, the underlying problem of assembling sequence fragments is computationally hard and many technical factors and limitations complicate obtaining the complete sequence of a genome. Many genomes are left in a draft state, in which each chromosome is represented by a set of sequences with partial information on their relative order. Recently, some approaches have been proposed to compare draft genomes by comparing paths in de Bruijn graphs, which are constructed by many practical genome assemblers. In this article we describe in more detail a method for comparing genomes represented as succinct colored de Bruijn graphs directly and without resorting to sequence alignments, called (texttt {gcBB}), that evaluates the entropy and expectation measures based on the Burrows-Wheeler Similarity Distribution. We also introduce an improved version of (texttt {gcBB}), called (texttt {multi-gcBB}), that improves the time and space performance considerably through the selection of different data structures. We have compared phylogenies of 12 Drosophila species obtained by other methods to those obtained with (texttt {gcBB}), achieving promising results.
{"title":"Comparative genomics with succinct colored de Bruijn graphs","authors":"Lucas P. Ramos, Felipe A. Louza, Guilherme P. Telles","doi":"10.1007/s00236-024-00467-7","DOIUrl":"10.1007/s00236-024-00467-7","url":null,"abstract":"<div><p>DNA technologies have evolved significantly in the past years enabling the sequencing of a large number of genomes in a short time. Nevertheless, the underlying problem of assembling sequence fragments is computationally hard and many technical factors and limitations complicate obtaining the complete sequence of a genome. Many genomes are left in a draft state, in which each chromosome is represented by a set of sequences with partial information on their relative order. Recently, some approaches have been proposed to compare draft genomes by comparing paths in de Bruijn graphs, which are constructed by many practical genome assemblers. In this article we describe in more detail a method for comparing genomes represented as succinct colored de Bruijn graphs directly and without resorting to sequence alignments, called <span>(texttt {gcBB})</span>, that evaluates the entropy and expectation measures based on the Burrows-Wheeler Similarity Distribution. We also introduce an improved version of <span>(texttt {gcBB})</span>, called <span>(texttt {multi-gcBB})</span>, that improves the time and space performance considerably through the selection of different data structures. We have compared phylogenies of 12 Drosophila species obtained by other methods to those obtained with <span>(texttt {gcBB})</span>, achieving promising results.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given a text and a pattern over an alphabet, the classic exact matching problem searches for all occurrences of the pattern in the text. Unlike exact matching, order-preserving pattern matching (OPPM) considers the relative order of elements, rather than their exact values. In this paper, we propose efficient algorithms for the OPPM problem using the “duel-and-sweep” paradigm. For a pattern of length m and a text of length n, our serial algorithm runs in (O(n + mlog m)) time, and our parallel algorithm runs in (O(log ^2 m)) time and (O(n log ^2 m)) work with (O(log m)) time and (O(m log m)) work pattern preprocessing on the Priority Concurrent Read Concurrent Write Parallel Random-Access Machines (P-CRCW PRAM).
给定一段文本和一个字母表上的模式,经典的精确匹配问题是搜索文本中模式的所有出现次数。与精确匹配不同,保序模式匹配(OPPM)考虑的是元素的相对顺序,而不是它们的精确值。在本文中,我们提出了使用 "决斗和扫荡 "范式来解决 OPPM 问题的高效算法。对于长度为 m 的模式和长度为 n 的文本,我们的串行算法运行时间为 (O(n + mlog m))、而我们的并行算法在优先并发读取并发写入并行随机存取机(P-CRCW PRAM)上的运行时间为(O(log ^2 m)),工作模式预处理时间为(O(log m)),工作模式预处理时间为(O(n log ^2 m))。
{"title":"Serial and parallel algorithms for order-preserving pattern matching based on the duel-and-sweep paradigm","authors":"Davaajav Jargalsaikhan, Diptarama Hendrian, Yohei Ueki, Ryo Yoshinaka, Ayumi Shinohara","doi":"10.1007/s00236-024-00464-w","DOIUrl":"10.1007/s00236-024-00464-w","url":null,"abstract":"<div><p>Given a text and a pattern over an alphabet, the classic exact matching problem searches for all occurrences of the pattern in the text. Unlike exact matching, <i>order-preserving pattern matching</i> (OPPM) considers the relative order of elements, rather than their exact values. In this paper, we propose efficient algorithms for the OPPM problem using the “duel-and-sweep” paradigm. For a pattern of length <i>m</i> and a text of length <i>n</i>, our serial algorithm runs in <span>(O(n + mlog m))</span> time, and our parallel algorithm runs in <span>(O(log ^2 m))</span> time and <span>(O(n log ^2 m))</span> work with <span>(O(log m))</span> time and <span>(O(m log m))</span> work pattern preprocessing on the Priority Concurrent Read Concurrent Write Parallel Random-Access Machines (P-CRCW PRAM).</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"61 4","pages":"415 - 444"},"PeriodicalIF":0.4,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-23DOI: 10.1007/s00236-024-00465-9
Shunsuke Inenaga
The linear-size suffix tries (LSTries) (Crochemore et al. in Theor Comput Sci 638:171–178, 2016) are a version of suffix trees in which the edge labels are single characters, yet are able to perform pattern matching queries in optimal time. Instead of explicitly storing the input text, LSTries have some extra non-branching internal nodes called type-2 nodes. The extended techniques are then used in the linear-size compact directed acyclic word graphs (LCDAWGs) (Takagi et al., in: SPIRE 2017, pp. 304–316, 2017), which can be stored with (O(textsf{el}(T)+textsf{er}(T))) space (i.e. without the text), where (textsf{el}(T)) and (textsf{er}(T)) are the numbers of left- and right-extensions of the maximal repeats in the input text string T, respectively. In this paper, we present simpler alternatives to the aforementioned indexing structures, called the simplified LSTries (simLSTries) and the simplified LCDAWGs (simLCDAWGs), in which most of the type-2 nodes are removed. In particular, our simLCDAWGs require only (O(textsf{er}(T))) space and work in a weaker model of computation (i.e. the pointer machine model). This contrasts the (O(textsf{er}(T)))-space CDAWG representation of Belazzougui and Cunial (in: Proceedings of the 24th international symposium on string processing and information retrieval, pp. 161–175, 2017), which works on the word RAM model.
线性大小后缀树(linear-size suffix tries,LSTries)(Crochemore 等人,载于 Theor Comput Sci 638:171-178, 2016)是后缀树的一个版本,其中的边标签是单字符,但却能在最佳时间内执行模式匹配查询。LSTries 不明确存储输入文本,而是有一些额外的非分支内部节点,称为 Type-2 节点。扩展技术随后被用于线性大小的紧凑有向无环词图(LCDAWGs)(Takagi et al、in: SPIRE 2017, pp. 304-316, 2017),它可以用 (O(textsf{el}(T)+textsf{er}(T)))空间存储(即不含文本),其中 (textsf{el}(T))和 (textsf{er}(T))分别是输入文本串 T 中最大重复次数的左扩展和右扩展的数量。在本文中,我们提出了上述索引结构的简化替代方案,称为简化 LSTries(simLSTries)和简化 LCDAWGs(simLCDAWGs),其中去除了大部分类型 2 节点。特别是,我们的 simLCDAWGs 只需要 (O(textsf{er}(T))) 空间,并且可以在较弱的计算模型(即指针机模型)中工作。这与 Belazzougui 和 Cunial 的 (O(textsf{er}(T)) )空间 CDAWG 表示(in:第 24 届字符串处理与信息检索国际研讨会论文集》(Proceedings of the 24th international symposium on string processing and information retrieval, pp.
{"title":"Linear-size suffix tries and linear-size CDAWGs simplified and improved","authors":"Shunsuke Inenaga","doi":"10.1007/s00236-024-00465-9","DOIUrl":"10.1007/s00236-024-00465-9","url":null,"abstract":"<div><p>The <i>linear-size suffix tries</i> (<i>LSTries</i>) (Crochemore et al. in Theor Comput Sci 638:171–178, 2016) are a version of suffix trees in which the edge labels are single characters, yet are able to perform pattern matching queries in optimal time. Instead of explicitly storing the input text, LSTries have some extra non-branching internal nodes called <i>type-2</i> nodes. The extended techniques are then used in the <i>linear-size compact directed acyclic word graphs</i> (<i>LCDAWGs</i>) (Takagi et al., in: SPIRE 2017, pp. 304–316, 2017), which can be stored with <span>(O(textsf{el}(T)+textsf{er}(T)))</span> space (i.e. without the text), where <span>(textsf{el}(T))</span> and <span>(textsf{er}(T))</span> are the numbers of left- and right-extensions of the maximal repeats in the input text string <i>T</i>, respectively. In this paper, we present simpler alternatives to the aforementioned indexing structures, called the <i>simplified LSTries</i> (<i>simLSTries</i>) and the <i>simplified LCDAWGs</i> (<i>simLCDAWGs</i>), in which most of the type-2 nodes are removed. In particular, our simLCDAWGs require only <span>(O(textsf{er}(T)))</span> space and work in a weaker model of computation (i.e. the pointer machine model). This contrasts the <span>(O(textsf{er}(T)))</span>-space CDAWG representation of Belazzougui and Cunial (in: Proceedings of the 24th international symposium on string processing and information retrieval, pp. 161–175, 2017), which works on the word RAM model.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"61 4","pages":"445 - 468"},"PeriodicalIF":0.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-15DOI: 10.1007/s00236-024-00463-x
Koustav De, Harshil Mittal, Palash Dey, Neeldhara Misra
The Kemeny method is one of the popular tools for rank aggregation. However, computing an optimal Kemeny ranking is (textsf{NP})-hard. Consequently, the computational task of finding a Kemeny ranking has been studied under the lens of parameterized complexity with respect to many parameters. We study the parameterized complexity of the problem of computing all distinct Kemeny rankings. We consider the target Kemeny score, number of candidates, average distance of input rankings, maximum range of any candidate, and unanimity width as our parameters. For all these parameters, we already have (textsf{FPT}) algorithms. We find that any desirable number of Kemeny rankings can also be found without substantial increase in running time. We also present (textsf{FPT}) approximation algorithms for Kemeny rank aggregation with respect to these parameters.
{"title":"Parameterized aspects of distinct Kemeny rank aggregation","authors":"Koustav De, Harshil Mittal, Palash Dey, Neeldhara Misra","doi":"10.1007/s00236-024-00463-x","DOIUrl":"10.1007/s00236-024-00463-x","url":null,"abstract":"<div><p>The Kemeny method is one of the popular tools for rank aggregation. However, computing an optimal Kemeny ranking is <span>(textsf{NP})</span>-hard. Consequently, the computational task of finding a Kemeny ranking has been studied under the lens of parameterized complexity with respect to many parameters. We study the parameterized complexity of the problem of computing all distinct Kemeny rankings. We consider the target Kemeny score, number of candidates, average distance of input rankings, maximum range of any candidate, and unanimity width as our parameters. For all these parameters, we already have <span>(textsf{FPT})</span> algorithms. We find that any desirable number of Kemeny rankings can also be found without substantial increase in running time. We also present <span>(textsf{FPT})</span> approximation algorithms for Kemeny rank aggregation with respect to these parameters.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"61 4","pages":"401 - 414"},"PeriodicalIF":0.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-10DOI: 10.1007/s00236-024-00462-y
Pamela Fleischmann, Lukas Haschke, Tim Löck, Dirk Nowotka
Word-representable graphs were introduced in 2008 by Kitaev and Pyatkin in the context of semigroup theory. Graphs are called word-representable if there exists a word with the graph’s nodes as letters such that the letters in the word alternate iff there is an edge between them in the graph. Until today numerous works investigated the word-representability of graphs but mostly from the graph perspective. In this work, we change the perspective to the words, i.e., we take classes of words and investigate the represented graphs. Our first subject of interest are the conjugates of words: we determine exactly which graphs are represented if we rotate the word. Afterwards, we look at k-local words introduced by Day et al. (FSTTCS LIPIcs, 2017) in order to gain more insights into this class of words. Here, we investigate especially which graphs are represented by 1-local words. Lastly, we prove that the language of all words representing a graph is regular. We were also able to characterise k-representable graphs, solving an open problem.
词可表示图是 Kitaev 和 Pyatkin 于 2008 年在半群理论的背景下提出的。如果存在一个以图的节点为字母的单词,且单词中的字母交替出现在图中,则该图被称为单词可表示图。迄今为止,研究图的单词可表示性的著作不胜枚举,但大多是从图的角度进行研究的。在这项工作中,我们将视角转向单词,即从单词的类别出发,研究其所代表的图。我们首先关注的是单词的共轭词:如果旋转单词,我们就能准确地确定哪些图被表示出来。之后,我们研究了 Day 等人(FSTTCS LIPIcs, 2017)引入的 k 本地单词,以深入了解这类单词。在这里,我们特别研究了哪些图是由 1 本地词表示的。最后,我们证明所有表示图的词的语言都是有规律的。我们还能够表征 k 可表示图,解决了一个未决问题。
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