Unit interval vertex deletion: Fewer vertices are relevant

Ke, Yuping; Cao, Yixin; Ouyang, Xiating; Li, Wenjun; Wang, Jianxin

doi:10.1016/j.jcss.2018.01.001

Cited by 8 publications

(3 citation statements)

References 21 publications

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“…Polynomial kernels for unit interval completion [2] and unit interval vertex deletion [13] have been known for a while. Using the approximation algorithm of Theorem 1.2, we [19] recently developed an O(k 4 )-vertex kernel for unit interval vertex deletion, improving from the O(k 53 ) one of Fomin et al [13]. We conjecture that the unit interval edge deletion problem also has a small polynomial kernel.…”

Section: Discussionmentioning

confidence: 81%

Unit interval editing is fixed-parameter tractable

Cao

2017

Information and Computation

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Given a graph G and integers k 1 , k 2 , and k 3 , the unit interval editing problem asks whether G can be transformed into a unit interval graph by at most k 1 vertex deletions, k 2 edge deletions, and k 3 edge additions. We give an algorithm solving this problem in time 2 O(k log k) · (n + m), where k := k 1 + k 2 + k 3 , and n, m denote respectively the numbers of vertices and edges of G. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations.Our algorithm implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time O(4 k · (n + m)). Another result is an O(6 k · (n + m))-time algorithm for the unit interval vertex deletion problem, significantly improving the algorithm of van 't Hof and Villanger, which runs in time O(6 k · n 6 ).

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Section: Discussionmentioning

confidence: 81%

Unit interval editing is fixed-parameter tractable

Cao

2017

Information and Computation

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“…We will aggregate these factors and construct a general prediction model to the resolve reserve prediction problem for bank outlets. We also will consider how to use new techniques to improve the predicting performances, such as parameterized algorithm [16,17] and matrix completion [18,19] .…”

Section: Discussionmentioning

confidence: 99%

LSTM based reserve prediction for bank outlets

Liu

Dong

et al. 2019

Tinshhua Sci. Technol.

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Reserve allocation is a significant problem faced by commercial banking businesses every day. To satisfy the cash requirement of customers and abate the vault cash pressure, commercial banks need to appropriately allocate reserves for each bank outlet. Excessive reserve would impact the revenue of bank outlets. Low reserves cannot guarantee the successful operation of bank outlets. Considering the reserve requirement is effected by the past cash balance, we deal the reserve allocation problem as a time series prediction problem, and the Long Short Time Memory (LSTM) network is adapted to solve it. In addition, the proposed LSTM prediction model regards date property, which can affect the cash balance, as a primary factor. The experiment results show that our method outperforms some existing traditional methods.

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“…, where each part is either a biclique or an independent set, and each set has edges only in the neighboring parts. The complete bipartite decomposition is similar to the clique partition used by Ke et al [23] for designing a polynomial kernel for vertex deletion to proper interval graphs.…”

Section: Methodsmentioning

confidence: 99%

A Polynomial Kernel for Bipartite Permutation Vertex Deletion

et al. 2022

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In a permutation graph, vertices represent the elements of a permutation, and edges represent pairs of elements that are reversed by the permutation. In the Permutation Vertex Deletion problem, given an undirected graph G and an integer k, the objective is to test whether there exists a vertex subset S ⊆ V (G) such that |S| ≤ k and G − S is a permutation graph. The parameterized complexity of Permutation Vertex Deletion is a well-known open problem. Bożyk et al. [IPEC 2020] initiated a study towards this problem by requiring that G − S be a bipartite permutation graph (a permutation graph that is bipartite). They called this the Bipartite Permutation Vertex Deletion (BPVD) problem. They showed that the problem admits a factor 9-approximation algorithm as well as a fixed parameter tractable (FPT) algorithm running in time O(9 k |V (G)| 9 ). And they posed the question whether BPVD admits a polynomial kernel.We resolve this question in the affirmative by designing a polynomial kernel for BPVD. In particular, we obtain the following: Given an instance (G, k) of BPVD, in polynomial time we obtain an equivalent instance (G ′ , k ′ ) of BPVD such that k ′ ≤ k, and |V (G ′ )| + |E(G ′ )| ≤ k O(1) .

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Unit interval vertex deletion: Fewer vertices are relevant

Cited by 8 publications

References 21 publications

Unit interval editing is fixed-parameter tractable

Unit interval editing is fixed-parameter tractable

LSTM based reserve prediction for bank outlets

A Polynomial Kernel for Bipartite Permutation Vertex Deletion

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