Pub Date : 2022-03-06DOI: 10.33048/daio.2022.29.727
S. Selezneva
{"title":"On complexity of searching for periods of functions given by polynomials over a prime field","authors":"S. Selezneva","doi":"10.33048/daio.2022.29.727","DOIUrl":"https://doi.org/10.33048/daio.2022.29.727","url":null,"abstract":"","PeriodicalId":126663,"journal":{"name":"Diskretnyi analiz i issledovanie operatsii","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132506167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-01DOI: 10.33048/daio.2021.28.710
A. G. Klyuchikov, M. Vyalyi
— We describe a Win/Win algorithm that produces in time polynomial in the size of a graph G and a given parameter k either a spanning tree with at least k + 1 leaves or a path decomposition of width at most k . This algorithm is optimal due to the path decomposition theorem.
{"title":"A win-win algorithm for the $(k+1)$-LST/$k$-pathwidth problem","authors":"A. G. Klyuchikov, M. Vyalyi","doi":"10.33048/daio.2021.28.710","DOIUrl":"https://doi.org/10.33048/daio.2021.28.710","url":null,"abstract":"— We describe a Win/Win algorithm that produces in time polynomial in the size of a graph G and a given parameter k either a spanning tree with at least k + 1 leaves or a path decomposition of width at most k . This algorithm is optimal due to the path decomposition theorem.","PeriodicalId":126663,"journal":{"name":"Diskretnyi analiz i issledovanie operatsii","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129176124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-01DOI: 10.33048/daio.2021.28.715
V. A. Voblyi
— We deduce the asymptotics for the number of labeled connected series-parallel k -cyclic graphs with large order and fi xed number k . We prove that almost all labeled series-parallel k -cyclic connected graphs without bridges for fi xed k are blocks
{"title":"Asymptotic enumeration of labeled series-parallel $k$-cyclic bridgeless graphs","authors":"V. A. Voblyi","doi":"10.33048/daio.2021.28.715","DOIUrl":"https://doi.org/10.33048/daio.2021.28.715","url":null,"abstract":"— We deduce the asymptotics for the number of labeled connected series-parallel k -cyclic graphs with large order and fi xed number k . We prove that almost all labeled series-parallel k -cyclic connected graphs without bridges for fi xed k are blocks","PeriodicalId":126663,"journal":{"name":"Diskretnyi analiz i issledovanie operatsii","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130339638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-03DOI: 10.33048/daio.2021.28.694
N. N. Tyunin
{"title":"The problems of non-convex quadratic programming related to phased antenna arrays optimization","authors":"N. N. Tyunin","doi":"10.33048/daio.2021.28.694","DOIUrl":"https://doi.org/10.33048/daio.2021.28.694","url":null,"abstract":"","PeriodicalId":126663,"journal":{"name":"Diskretnyi analiz i issledovanie operatsii","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122016688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-03DOI: 10.33048/daio.2021.28.667
O. Duginov
{"title":"A weighted perfect matching with constraints on weights of its parts","authors":"O. Duginov","doi":"10.33048/daio.2021.28.667","DOIUrl":"https://doi.org/10.33048/daio.2021.28.667","url":null,"abstract":"","PeriodicalId":126663,"journal":{"name":"Diskretnyi analiz i issledovanie operatsii","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114941657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-01DOI: 10.33048/daio.2021.28.709
A. Makhnev, M. P. Golubyatnikov
— We consider Q -polynomial graphs of diameter 4 . Alongside the in fi nite series of intersection arrays { m (2 m + 1) , ( m − 1)(2 m + 1) , m 2 , m ; 1 , m, m − 1 , m (2 m + 1) } , the following admissible intersection arrays of Q -polynomial graphs of diameter 4 with at most 4096 vertices are known: { 5 , 4 , 4 , 3; 1 , 1 , 2 , 2 } (the odd graph on 9 vertices), { 9 , 8 , 7 , 6; 1 , 2 , 3 , 4 } (the folded 9 -cube), { 36 , 21 , 10 , 3; 1 , 6 , 15 , 28 } (the half 9 -cube), and { 53 , 40 , 28 , 16; 1 , 4 , 10 , 28 } . We prove that there is no distance-regular graphs with intersection array { 53 , 40 , 28 , 16; 1 , 4 , 10 , 28 } . DOI
-我们考虑直径为4的Q -多项式图。在相交数组{m (2 m + 1)， (m−1)(2 m + 1)， m2, m;1, m, m−1,m (2m + 1)}，则已知直径为4且最多有4096个顶点的Q -多项式图的下列可容许相交数组:{5,4,4,3;1,1,2,2}(有9个顶点的奇图)，{9,8,7,6;1,2,3,4}(折叠后的9 -立方体)，{36,21,10,3;1, 6, 15, 28}(半9立方)和{53,40,28,16;1,4,10,28}。证明了不存在相交数组为{53,40,28,16;1,4,10,28}。DOI
{"title":"On nonexistence of distance regular graphs with the intersection array ${53,40,28,16;1,4,10,28}$","authors":"A. Makhnev, M. P. Golubyatnikov","doi":"10.33048/daio.2021.28.709","DOIUrl":"https://doi.org/10.33048/daio.2021.28.709","url":null,"abstract":"— We consider Q -polynomial graphs of diameter 4 . Alongside the in fi nite series of intersection arrays { m (2 m + 1) , ( m − 1)(2 m + 1) , m 2 , m ; 1 , m, m − 1 , m (2 m + 1) } , the following admissible intersection arrays of Q -polynomial graphs of diameter 4 with at most 4096 vertices are known: { 5 , 4 , 4 , 3; 1 , 1 , 2 , 2 } (the odd graph on 9 vertices), { 9 , 8 , 7 , 6; 1 , 2 , 3 , 4 } (the folded 9 -cube), { 36 , 21 , 10 , 3; 1 , 6 , 15 , 28 } (the half 9 -cube), and { 53 , 40 , 28 , 16; 1 , 4 , 10 , 28 } . We prove that there is no distance-regular graphs with intersection array { 53 , 40 , 28 , 16; 1 , 4 , 10 , 28 } . DOI","PeriodicalId":126663,"journal":{"name":"Diskretnyi analiz i issledovanie operatsii","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124201390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-03DOI: 10.33048/daio.2020.27.677
A. Glebov, S. G. Toktokhoeva
— In 2005, Kaplan et al. presented a polynomial-time algorithm with guaranteed approximation ratio 2 / 3 for the maximization version of the asymmetric TSP. In 2014, Glebov, Skretneva, and Zambalaeva constructed a similar algorithm with approximation ratio 2 / 3 and cubic runtime for the maximization version of the asymmetric 2 -PSP ( 2 -APSP-max), where it is required to fi nd two edge-disjoint Hamiltonian cycles of maximum total weight in a complete directed weighted graph. The goal of this paper is to construct a similar algorithm for the more general m -APSP-max in the asymmetric case and justify an approximation ratio for this algorithm that tends to 2 / 3 as n grows and the runtime complexity estimate O ( mn 3 ) . DOI
{"title":"A polynomial algorithm with asymptotic ratio $2/3$ for the asymmetric maximization version of the $m$-PSP","authors":"A. Glebov, S. G. Toktokhoeva","doi":"10.33048/daio.2020.27.677","DOIUrl":"https://doi.org/10.33048/daio.2020.27.677","url":null,"abstract":"— In 2005, Kaplan et al. presented a polynomial-time algorithm with guaranteed approximation ratio 2 / 3 for the maximization version of the asymmetric TSP. In 2014, Glebov, Skretneva, and Zambalaeva constructed a similar algorithm with approximation ratio 2 / 3 and cubic runtime for the maximization version of the asymmetric 2 -PSP ( 2 -APSP-max), where it is required to fi nd two edge-disjoint Hamiltonian cycles of maximum total weight in a complete directed weighted graph. The goal of this paper is to construct a similar algorithm for the more general m -APSP-max in the asymmetric case and justify an approximation ratio for this algorithm that tends to 2 / 3 as n grows and the runtime complexity estimate O ( mn 3 ) . DOI","PeriodicalId":126663,"journal":{"name":"Diskretnyi analiz i issledovanie operatsii","volume":"49 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129175082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-05DOI: 10.33048/daio.2020.27.631
I. Borisova
— We consider the computational complexity of one extremal problem of choosing a subset of p points from some given 2 -clustering of a fi nite set in a metric space. The chosen subset of points has to describe the given clusters in the best way from the viewpoint of some geometric criterion. This is a formalization of an applied problem of data mining which consists in fi nding a subset of typical representatives of a dataset composed of two classes based on the function of rival similarity. The problem is proved to be NP-hard. To this end, we polynomially reduce to the problem one of the well-known problems NP-hard in the strong sense, the p -median problem.
{"title":"Computational complexity of the problem of choosing typical representatives in a 2-clustering of a finite set of points in a metric space","authors":"I. Borisova","doi":"10.33048/daio.2020.27.631","DOIUrl":"https://doi.org/10.33048/daio.2020.27.631","url":null,"abstract":"— We consider the computational complexity of one extremal problem of choosing a subset of p points from some given 2 -clustering of a fi nite set in a metric space. The chosen subset of points has to describe the given clusters in the best way from the viewpoint of some geometric criterion. This is a formalization of an applied problem of data mining which consists in fi nding a subset of typical representatives of a dataset composed of two classes based on the function of rival similarity. The problem is proved to be NP-hard. To this end, we polynomially reduce to the problem one of the well-known problems NP-hard in the strong sense, the p -median problem.","PeriodicalId":126663,"journal":{"name":"Diskretnyi analiz i issledovanie operatsii","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124779227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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