Shortest Reconfiguration of Colorings Under Kempe Changes

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Algorithms for Coloring Reconfiguration Under Recolorability Constraints

Coloring reconfiguration is one of the most well-studied reconfiguration problems. In the problem, we are given two (vertex-)colorings of a graph using at most k colors, and asked to determine whether there exists a transformation between them by recoloring only a single vertex at a time, while maintaining a k-coloring throughout. It is known that this problem is solvable in linear time for any graph if k = 4. In this paper, we further investigate the problem from the viewpoint of recolorability constraints, which forbid some pairs of colors to be recolored directly. More specifically, the recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color, and each edge in R represents a pair of colors that can be recolored directly. In this paper, we give a linear-time algorithm to solve the problem under such a recolorability constraint if R is of maximum degree at most two. In addition, we show that the minimum number of recoloring steps required for a desired transformation can be computed in linear time for a yes-instance. We note that our results generalize the known positive ones for coloring reconfiguration

Response of germination and seedling growth to soil particle size of three herbaceous perennials on alpine zone of Mt. Fuji

Polygonum cuspidatum, P. weyrichii and Artemisia pedunculosa are herbaceous perennials in the alpine zone on Mt. Fuji. The effect of soil particle size on seed germination and seedling growth of these species was investigated. In the experiment three different particle size soils (large particle size LPS, medium particle size MPS, and small particle size SPS) were used. The other experiment was designed under three different watering intervals (every day, every two days, and every four days). Soil particle size had a great impact on seed germination and seedling growth. The highest percentage of seeds germinated in SPS and lowest in LPS soil, irrespective of the species. In the case of A. pedunculosa there was no significant difference of seed germination between SPS and MPS soils. However, the other two species had significantly reduced percentages of seed germination with increasing soil particle size. The maximum root length of seedlings was significantly longer in LPS and MPS compared to the SPS soil group, for all species. The number of root tips was increased with decreasing soil particle size, irrespective of the species. Further, larger aboveground biomass was found in seedlings of SPS than those of LPS and MPS. A. pedunculosa showed a slightly different pattern of seed germination and seedling growth compared to the two Polygonum species. Seed germination of A. pedunculosa was comparatively independent of soil particle size, and it may have conservative water use strategy. On the other hand, seed germination of Polygonum species was highly affected by the soil particle size, and those species may adapt to the water deficit condition by taking up water from deeper soil

Intrapulmonary metastasis of non–small cell lung cancer: A prognostic assessment

AbstractObjective: According to the revised TNM classification in 1997, intrapulmonary metastasis within the same lobe of the primary tumor is designated as T4 and intrapulmonary metastasis in a different lobe is M1. However, their prognostic implications remain unclear. To assess their prognoses, we retrospectively analyzed the postoperative survival of patients with and without intrapulmonary metastasis. Methods: From January 1982 to December 1996, 2340 patients with non–small cell lung cancer underwent surgical resection. The survival of patients having complete resection (n = 1534) was analyzed according to their intrapulmonary metastasis status: patients without intrapulmonary metastasis (n = 1393), those with metastasis in the same lobe (n = 105), and those with metastasis in a different lobe (n = 18). For comparison, patients with T4 disease without intrapulmonary metastasis in the same lobe (n = 54) and those with M1 disease without metastasis in a different lobe (distant M1, n = 18) were also analyzed. Results: The overall 5-year survivals were as follows: no intrapulmonary metastasis, 60%; stage T4 disease with no intrapulmonary metastasis, 34%; pulmonary metastasis in the same lobe, 34%; pulmonary metastasis in a different lobe, 11%; and distant M1, 6%. The differences in survival between patients with no pulmonary metastasis and those with metastasis in the same lobe (P <.001, log-rank test) and between patients with metastasis in the same lobe and those with distant M1 (P <.001) were significant. In contrast, there was no significant difference between patients with metastasis in the same lobe and those with T4 disease and no intrapulmonary metastasis or between patients with metastasis to a different lobe and those with distant M1. Conclusions: Prognostically, intrapulmonary metastasis within the same lobe of the primary tumor was comparable with T4 and that in a different lobe was comparable with M1. In terms of postoperative prognosis, the revised TNM classification for intrapulmonary metastasis seems to be appropriate.J Thorac Cardiovasc Surg 2001;122:24-

Fixed-Parameter Algorithms for Graph Constraint Logic

Non-deterministic constraint logic (NCL) is a simple model of computation based on orientations of a constraint graph with edge weights and vertex demands. NCL captures PSPACE and has been a useful tool for proving algorithmic hardness of many puzzles, games, and reconfiguration problems. In particular, its usefulness stems from the fact that it remains PSPACE-complete even under severe restrictions of the weights (e.g., only edge-weights one and two are needed) and the structure of the constraint graph (e.g., planar AND/OR graphs of bounded bandwidth). While such restrictions on the structure of constraint graphs do not seem to limit the expressiveness of NCL, the building blocks of the constraint graphs cannot be limited without losing expressiveness: We consider as parameters the number of weight-one edges and the number of weight-two edges of a constraint graph, as well as the number of AND or OR vertices of an AND/OR constraint graph. We show that NCL is fixed-parameter tractable (FPT) for any of these parameters. In particular, for NCL parameterized by the number of weight-one edges or the number of AND vertices, we obtain a linear kernel. It follows that, in a sense, NCL as introduced by Hearn and Demaine is defined in the most economical way for the purpose of capturing PSPACE

ESTIMATION OF GROUND REACTION FORCES DURING RUNNING USING INERTIAL MEASUREMENT UNITS AND ARTIFICIAL NEURAL NETWORKS

The purpose of this study was to develop a system to estimate ground reaction forces during running using inertial measurement units and artificial neural networks. Kinematics of the pelvis and feet and ground reaction forces were measured using an inertial measurement system developed by Casio and Kistler force plates from seventy-nine runners (57 males and 22 females). Two long short-term memory based neural networks were used to estimate the instants of foot-strike and toe-off, and anteroposterior and vertical ground reaction forces from the triaxial accelerations and angular velocities measured by inertial measurement units fixed to the pelvis and foot of support leg. Although there are some limitations due to the small sample size, the results of this study showed the potential of estimating the ground reaction forces during running using a small number of inertial measurement units and artificial neural networks

Reconfiguration of Spanning Trees with Degree Constraint or Diameter Constraint

We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields that such a transformation always exists if we have no constraints on spanning trees. In this paper, we wish to find a transformation which passes through only spanning trees satisfying some constraint. Our focus is bounding either the maximum degree or the diameter of spanning trees, and we give the following results. The problem with a lower bound on maximum degree is solvable in polynomial time, while the problem with an upper bound on maximum degree is PSPACE-complete. The problem with a lower bound on diameter is NP-hard, while the problem with an upper bound on diameter is solvable in polynomial time