The Experts below are selected from a list of 8604 Experts worldwide ranked by ideXlab platform
Alexey N Medvedev - One of the best experts on this subject based on the ideXlab platform.
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small Cycles generalized prisms and Hamiltonian Cycles in the bubble sort graph
Information Processing Letters, 2021Co-Authors: Elena V Konstantinova, Alexey N MedvedevAbstract:Abstract The Bubble-sort graph B S n , n ⩾ 2 , is a Cayley graph over the symmetric group S y m n generated by transpositions from the set { ( 12 ) , ( 23 ) , … , ( n − 1 n ) } . It is a bipartite graph containing all even Cycles of length l, where 4 ⩽ l ⩽ n ! . We give an explicit combinatorial characterization of all its 4- and 6-Cycles. Based on this characterization, we define generalized prisms in B S n , n ⩾ 5 , and present a new approach to construct a Hamiltonian Cycle based on these generalized prisms.
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a note on small Cycles in the bubble sort graph
2019Co-Authors: Elena V Konstantinova, Alexey N MedvedevAbstract:The Bubble-sort graph $BS_n,\,n\geqslant 2$, is a Cayley graph over the symmetric group $Sym_n$ generated by transpositions from the set $\{(1 2), (2 3),\ldots, (n-1 n)\}$. It is a bipartite graph containing all even Cycles of length $\ell$, where $4\leqslant \ell\leqslant n!$. We give an explicit combinatorial characterization of all its $4$- and $6$-Cycles. Based on this characterization, we define generalized prisms in $BS_n,\,n\geqslant 5$, and present a new approach to construct a Hamiltonian Cycle based on these generalized prisms.
Karol Wegrzycki - One of the best experts on this subject based on the ideXlab platform.
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Hamiltonian Cycle parameterized by treedepth in single exponential time and polynomial space
Workshop on Graph-Theoretic Concepts in Computer Science, 2020Co-Authors: Jesper Nederlof, Michal Pilipczuk, Celine M F Swennenhuis, Karol WegrzyckiAbstract:For many algorithmic problems on graphs of treewidth \(t\), a standard dynamic programming approach gives an algorithm with time and space complexity \(2^{\mathcal {O}(t)}\cdot n^{\mathcal {O}(1)}\). It turns out that when one considers the more restrictive parameter treedepth, it is often the case that a variation of this technique can be used to reduce the space complexity to polynomial, while retaining time complexity of the form \(2^{\mathcal {O}(d)}\cdot n^{\mathcal {O}(1)}\), where \(d\) is the treedepth. This transfer of methodology is, however, far from automatic. For instance, for problems with connectivity constraints, standard dynamic programming techniques give algorithms with time and space complexity \(2^{\mathcal {O}(t\log t)}\cdot n^{\mathcal {O}(1)}\) on graphs of treewidth \(t\), but it is not clear how to convert them into time-efficient polynomial space algorithms for graphs of low treedepth.
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Hamiltonian Cycle parameterized by treedepth in single exponential time and polynomial space
arXiv: Data Structures and Algorithms, 2020Co-Authors: Jesper Nederlof, Michal Pilipczuk, Celine M F Swennenhuis, Karol WegrzyckiAbstract:For many algorithmic problems on graphs of treewidth $t$, a standard dynamic programming approach gives an algorithm with time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. It turns out that when one considers the more restrictive parameter treedepth, it is often the case that a variation of this technique can be used to reduce the space complexity to polynomial, while retaining time complexity of the form $2^{\mathcal{O}(d)}\cdot n^{\mathcal{O}(1)}$, where $d$ is the treedepth. This transfer of methodology is, however, far from automatic. For instance, for problems with connectivity constraints, standard dynamic programming techniques give algorithms with time and space complexity $2^{\mathcal{O}(t\log t)}\cdot n^{\mathcal{O}(1)}$ on graphs of treewidth $t$, but it is not clear how to convert them into time-efficient polynomial space algorithms for graphs of low treedepth. Cygan et al. (FOCS'11) introduced the Cut&Count technique and showed that a certain class of problems with connectivity constraints can be solved in time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. Recently, Hegerfeld and Kratsch (STACS'20) showed that, for some of those problems, the Cut&Count technique can be also applied in the setting of treedepth, and it gives algorithms with running time $2^{\mathcal{O}(d)}\cdot n^{\mathcal{O}(1)}$ and polynomial space usage. However, a number of important problems eluded such a treatment, with the most prominent examples being Hamiltonian Cycle and Longest Path. In this paper we clarify the situation by showing that Hamiltonian Cycle, Hamiltonian Path, Long Cycle, Long Path, and Min Cycle Cover all admit $5^d\cdot n^{\mathcal{O}(1)}$-time and polynomial space algorithms on graphs of treedepth $d$. The algorithms are randomized Monte Carlo with only false negatives.
Wang Wenjie - One of the best experts on this subject based on the ideXlab platform.
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research on Hamiltonian Cycle based on path with interface
Computer Science, 2010Co-Authors: Wang WenjieAbstract:In order to find all Hamiltonian Cycles in a digraph,to begin with,it presented an encoding method for the power set,which converts the problem of Hamilton circuits into the computation of hierarchical matrix.Secondly,it estimated the complexity of algorithm with the proof of Xiaerci guess.Finally,it gave the exact algorithm for CTSP.
Yali Lv - One of the best experts on this subject based on the ideXlab platform.
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Hamiltonian Cycle and path embeddings in 3 ary n cubes based on k1 3 structure faults
Journal of Parallel and Distributed Computing, 2018Co-Authors: Yali LvAbstract:Abstract The k -ary n -cube is one of the most attractive interconnection networks for parallel and distributed computing system. In this paper, we investigate Hamiltonian Cycle and path embeddings in 3-ary n -cubes Q n 3 based on K 1 , 3 -structure faults, which means each faulty element is isomorphic to any connected subgraph of a connected graph K 1 , 3 . We show that for two arbitrary distinct healthy nodes of a faulty Q n 3 , there exists a fault-free Hamiltonian path connecting these two nodes if the number of faulty element is at most n − 2 and each faulty element is isomorphic to any connected subgraph of K 1 , 3 . We also show that there exists a fault-free Hamiltonian Cycle if the number of faulty element is at most n − 1 and each faulty element is isomorphic to any connected subgraph of K 1 , 3 . Then, we provide the simulation experiment to find a Hamiltonian Cycle and a Hamiltonian path in structure faulty 3-ary n -cubes and verify the theoretical results. These results mean that the 3-ary n -cube Q n 3 can tolerate up to 4 ( n − 2 ) faulty nodes such that Q n 3 − V ( F ) is still Hamiltonian and Hamiltonian-connected, where F denotes the faulty set of Q n 3 .
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Hamiltonian Cycle and Path Embeddings in 3-Ary n-Cubes Based on K1,2-Structure Faults
2016 IEEE Trustcom BigDataSE ISPA, 2016Co-Authors: Yali LvAbstract:The k-ary n-cube is one of the most attractive interconnection networks for parallel and distributed computing system. In this paper, we investigate Hamiltonian Cycle and path embeddings in 3-ary n-cubes Qn3 based on K1,2-structure faults, which means each faulty element is isomorphic to a connected graph K1,2 or a connected subgraph of the connected graph. We show that for two arbitrary distinct healthy nodes of a faulty Qn3, there exists a fault-free Hamiltonian path connecting these two nodes if the number of faulty element is at most n-2 and each faulty element is isomorphic to K1,2 or a connected subgraph of K1,2. We also show that there exists a fault-free Hamiltonian Cycle if the number of faulty element is at most n-1 and each faulty element is isomorphic to K1,2 or a connected subgraph of K1,2. These results mean that the 3-ary n-cube Q3n can tolerate up to 3(n - 2) faulty nodes such that Qn3 - V (F) is still Hamiltonian and Hamiltonian-connected, where F denotes the faulty set of Qn3.
Elena V Konstantinova - One of the best experts on this subject based on the ideXlab platform.
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small Cycles generalized prisms and Hamiltonian Cycles in the bubble sort graph
Information Processing Letters, 2021Co-Authors: Elena V Konstantinova, Alexey N MedvedevAbstract:Abstract The Bubble-sort graph B S n , n ⩾ 2 , is a Cayley graph over the symmetric group S y m n generated by transpositions from the set { ( 12 ) , ( 23 ) , … , ( n − 1 n ) } . It is a bipartite graph containing all even Cycles of length l, where 4 ⩽ l ⩽ n ! . We give an explicit combinatorial characterization of all its 4- and 6-Cycles. Based on this characterization, we define generalized prisms in B S n , n ⩾ 5 , and present a new approach to construct a Hamiltonian Cycle based on these generalized prisms.
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a note on small Cycles in the bubble sort graph
2019Co-Authors: Elena V Konstantinova, Alexey N MedvedevAbstract:The Bubble-sort graph $BS_n,\,n\geqslant 2$, is a Cayley graph over the symmetric group $Sym_n$ generated by transpositions from the set $\{(1 2), (2 3),\ldots, (n-1 n)\}$. It is a bipartite graph containing all even Cycles of length $\ell$, where $4\leqslant \ell\leqslant n!$. We give an explicit combinatorial characterization of all its $4$- and $6$-Cycles. Based on this characterization, we define generalized prisms in $BS_n,\,n\geqslant 5$, and present a new approach to construct a Hamiltonian Cycle based on these generalized prisms.
