Optimal Augmentation of a 2-Vertex-Connected Multigraph to a k-Edge-Connected and 3-Vertex-Connected Multigraph

Given an undirected multigraph G = (V, E) and two positive integers and k, we consider the problem of augmenting G by the smallest number of new edges to obtain an -edge-connected and k-vertex-connected multigraph. In this paper, we show that the problem can be solved in Õ(mn²) time for any fixed and k = 3 if an input multigraph G is 2-vertex-connected, where n = |V| and m is the number of pairs of adjacent vertices in G.     

What Underlies the White American Public's Negative Attitudes Toward Japan's Domestic Market?

Many have contended that the white American public's negative attitudes toward Japan's domestic market are caused by one or more of three categories: economic, ethnic, and cultural elements. To date, no study has examined the connections between these categories. A questionnaire survey was used to collect responses from 296 white college students. A multiple regression analysis found that only economic elements were responsible for the negative attitudes toward Japan's domestic market. Neither cultural nor ethnic elements were found responsible. However, the economic elements accounted for about 10% of the variance in negative attitudes, leaving the vast majority of the variance unexplained. These findings suggest that elements responsible for the white American public's negative attitudes toward Japan's domestic market are not as simple as previously assumed.     

Approximating the Minimum k-way Cut in a Graph via Minimum 3-way Cuts

For an edge weighted undirected graph G and an integer k > 2, a k-way cut is a set of edges whose removal leaves G with at least k components. We propose a simple approximation algorithm to the minimum k-way cut problem. It computes a nearly optimal k-way cut by using a set of minimum 3-way cuts. We show that the performance ratio of our algorithm is 2 – 3/k for an odd k and 2 – (3k – 4)/(k ² – k) for an even k. The running time is O(kmn ³ log(n ²/m)) where n and m are the numbers of vertices and edges respectively.     

Deterministic Õ(nm) Time Edge-Splitting in Undirected Graphs

This paper presents a deterministic O (nm log n + n2log2n) = Õ (nm) time algorithm for splitting off all edges incident to a vertex s of even degree in a multigraph G, where n and m are the numbers of vertices and links (= vertex pairs between which G has an edge) in G, respectively. Based on this, many graph algorithms using edge-splitting can run faster. For example, the edge-connectivity augmentation problem in an undirected multigraph can be solved in Õ (nm) time, which is an improvement over the previously known randomized Õ (n3) bound and deterministic Õ (n2m) bound.     

Relative humidity as an environmental factor determining the microhabitat of the nymphs of the rice brown planthopper,Nilaparvata lugens (St?l) (Homoptera: Delphacidae)

Summary Microhabitat of the nymphs and the adults of the rice brown, planthopper,Nilaparvata lugens is known to be the lower parts of rice plants. In this study, possible environmental factors determining the range of the microhabitat were experimentally analyzed by using the nymphs under laboratory conditions. Thirty individuals of the 1st or the 3rd instar nymphs were released to a potted rice plant covered with a transparent acrylic cylinder. When the top of the cylinder was kept opening (open condition), the temperatures in the cylinder were almost constant, and relative humidities in the cylinder decreased with the increase of the height from the water surface of the pot. In the open condition, most nymphs and all exuviae were found on the basal parts of rice plants where the humidity was more than ca. 90% r.h. When the top of the cylinder was kept closing with parafilm (closed condition), the temperatures in the cylinder were almost constant, and relative humidities in the cylinder were more than 95% r.h. In the closed condition, the nymphs and the exuviae were distributed sparsely to the whole parts of rice plants. In both of the open and the closed conditions, patterns of nymphal distributions on rice plants during the dark regime were the same as those during the light regime under 25±2°C and 16L∶8D. Four different temperatures ranging from 20°C to 35°C did not influence on the microhabitat in the open condition. It was concluded from the results that relative humidity is the important environmental factor to determine the microhabitat of the nymphs ofN. lugens which showed to prefer very humid condition more than ca. 90% r.h.     

Augmenting a Submodular and Posi-modular Set Function by a Multigraph

Given a finite set V and a set function , we consider the problem of constructing an undirected multigraph G = (V,E) such that the cut function together has value at least 2 for all non-empty and proper subsets of V. If f is intersecting submodular and posi-modular, and satisfies the tripartite inequality, then we show that such a multigraph G with the minimum number of edges can be found in time, where is the time to compute the value of f(X) for a subset .     

A Faster Algorithm for Computing Minimum 5-Way and 6-Way Cuts in Graphs

For an edge-weighted graph G with n vertices and m edges, the minimum k-way cut problem is to find a partition of the vertex set into k non-empty subsets so that the weight sum of edges between different subsets is minimized. For this problem with k = 5 and 6, we present a deterministic algorithm that runs in O(n^{k – 1}F(n, m)) = O(mn^k log (n²/m)) time, where F(n, m) denotes the time bound required to solve the maximum flow problem in G. The bounds Õ(mn⁵) for k = 5 and Õ(mn⁶) for k = 6 improve the previous best randomized bounds Õ(n⁸) and Õ(n¹⁰), respectively.     

Humid microenvironment prerequisite for the survival and growth of nymphs of the rice brown planthopper,Nilaparvata lugens (St?l) (Homoptera: Delphacidae)

Nymphs ofNilaparvata lugens were experimentally reared from the 2nd instar in a cage covering part of the leaf sheath of an individual rice plant grown in a Wagner pot. Plants were covered with the cage from the water surface of the pot to 10 cm above the surface (lower cage-group) or from 10 cm to 20 cm above the surface (upper cage-group). Temperatures measured at three different parts of the cage remained fairly constant in both groups at around 25°C (23.7–25.2°C in mean value). In the lower cage-group, relative humidities measured at the three heights in the cage in (76.3–90.5% in mean value) markedly increased with the approach to the water surface. The nymphs of this group, particularly during the molting period, aggregated close to the surface. Eighty-two percent of the released nymphs emerged in this group. Relative humidities measured at three heights of the upper cage-group were 69.5–72.7% in mean value, and all the nymphs in this group died within 3 days after their release although half of them stayed on the rice plants within 6 h after their release. The role of relative humidity as a limiting factor on the range of the microhabitat and the population density ofN. lugens in rice fields was discussed on the basis of the results.