The NP-hard Odd Cycle Transversal problem asks for a minimum vertex set whose removal from an undirected input graph $G$ breaks all odd cycles, and thereby yields a bipartite graph. The problem is well-known to be fixed-parameter tractable when parameterized by the size $k$ of the desired solution. It also admits a randomized kernelization of polynomial size, using the celebrated matroid toolkit by Kratsch and Wahlström. The kernelization guarantees a reduction in the total $\textit{size}$ of an input graph, but does not guarantee any decrease in the size of the solution to be sought; the latter governs the size of the search space for FPT algorithms parameterized by $k$. We investigate under which conditions an efficient algorithm can detect one or more vertices that belong to an optimal solution to Odd Cycle Transversal. By drawing inspiration from the popular $\textit{crown reduction}$ rule for Vertex Cover, and the notion of $\textit{antler decompositions}$ that was recently proposed for Feedback Vertex Set, we introduce a graph decomposition called $\textit{tight odd cycle cut}$ that can be used to certify that a vertex set is part of an optimal odd cycle transversal. While it is NP-hard to compute such a graph decomposition, we develop parameterized algorithms to find a set of at least $k$ vertices that belong to an optimal odd cycle transversal when the input contains a tight odd cycle cut certifying the membership of $k$ vertices in an optimal solution. The resulting algorithm formalizes when the search space for the solution-size parameterization of Odd Cycle Transversal can be reduced by preprocessing. To obtain our results, we develop a graph reduction step that can be used to simplify the graph to the point that the odd cycle cut can be detected via color coding.

We present fixed-parameter tractable (FPT) algorithms for two problems, Maximum Happy Set (MaxHS) and Densest k-Subgraph (DkS) - also known as Maximum Edge Happy Set. Given a graph G and an integer k, MaxHS asks for a set S of k vertices such that the number of happy vertices with respect to S is maximized, where a vertex v is happy if v and all its neighbors are in S. We show that MaxHS can be solved in time 𝒪(2^mw ⋅ mw ⋅ k² ⋅ |V(G)|) and 𝒪(8^cw ⋅ k² ⋅ |V(G)|), where mw and cw denote the modular-width and the clique-width of G, respectively. This answers the open questions on fixed-parameter tractability posed in [Asahiro et al., 2021]. The DkS problem asks for a subgraph with k vertices maximizing the number of edges. If we define happy edges as the edges whose endpoints are in S, then DkS can be seen as an edge-variant of MaxHS. In this paper we show that DkS can be solved in time f(nd)⋅|V(G)|^𝒪(1) and 𝒪(2^{cd}⋅ k² ⋅ |V(G)|), where nd and cd denote the neighborhood diversity and the cluster deletion number of G, respectively, and f is some computable function. This result implies that DkS is also fixed-parameter tractable by twin cover number.

A primary challenge in metagenomics is reconstructing individual microbial genomes from the mixture of short fragments created by sequencing. Recent work leverages the sparsity of the assembly graph to find r-dominating sets which enable rapid approximate queries through a dominator-centric graph partition. In this paper, we consider two problems related to reducing uncertainty and improving scalability in this setting.

Recently, in the medical care, in order to achieve micro manipulation, many robots are researched. This paper focuses macro-micro bilateral control system which is one of the micro manipulation robots. Macro-micro bilateral control system consists of position control and force control. Therefore, in this paper, in order to achieve high accuracy macro-micro bilateral control system, high accuracy position control and force control is implemented. Firstly, the high resolution encoder is used. A low friction structure is used to force control. In addition, nominal mass is important for accurate force observation. Therefore, identification of mass is proposed. Macro-micro bilateral control system is implemented with proposed structure and identified nominal mass.

Recently, real world haptics are researched. In this paper, the environment copying system is focused. The environment copying system is one of the real world haptics techniques. The environment copying system achieves saving and reproduction of real world environments haptic sensation. The environment copying system needs environment model. The environment model calculates environment reaction force. Thereby, haptic sensation reproduction is achieved. The conventional model consists of a pair of spring and damper. It can not reproduce oscillation of the environment. In this paper, the model based on wave equation is proposed. It can reproduce oscillation of the environment.