Classifying Subset Feedback Vertex Set for H-free graphs

In the FEEDBACK VERTEX SET problem, we aim to find a small set S of vertices in a graph intersecting every cycle. The SUBSET FEEDBACK VERTEX SET problem requires S to intersect only those cycles that include a vertex of some specified set T. We also consider the WEIGHTED SUBSET FEEDBACK VERTEX SET problem, where each vertex u has weight w(u)>0 and we ask that S has small weight. By combining known NP-hardness results with new polynomial-time results we prove full complexity dichotomies for SUBSET FEEDBACK VERTEX SET and WEIGHTED SUBSET FEEDBACK VERTEX SET for H-free graphs, that is, graphs that do not contain a graph H as an induced subgraph

Metro-Line Crossing Minimization: Hardness, Approximations, and Tractable Cases

Crossing minimization is one of the central problems in graph drawing. Recently, there has been an increased interest in the problem of minimizing crossings between paths in drawings of graphs. This is the metro-line crossing minimization problem (MLCM): Given an embedded graph and a set L of simple paths, called lines, order the lines on each edge so that the total number of crossings is minimized. So far, the complexity of MLCM has been an open problem. In contrast, the problem variant in which line ends must be placed in outermost position on their edges (MLCM-P) is known to be NP-hard. Our main results answer two open questions: (i) We show that MLCM is NP-hard. (ii) We give an $O(\sqrt{\log |L|})$-approximation algorithm for MLCM-P

Computing Schematic Layouts for Spatial Hypergraphs on Concentric Circles and Grids

Set systems can be visualized in various ways. An important distinction between techniques is whether the elements have a spatial location that is to be used for the visualization; for example, the elements are cities on a map. Strictly adhering to such location may severely limit the visualization and force overlay, intersections and other forms of clutter. On the other hand, completely ignoring the spatial dimension omits information and may hide spatial patterns in the data. We study layouts for set systems (or hypergraphs) in which spatial locations are displaced onto concentric circles or a grid, to obtain schematic set visualizations. We investigate the tractability of the underlying algorithmic problems adopting different optimization criteria (e.g. crossings or bends) for the layout structure, also known as the support of the hypergraph. Furthermore, we describe a simulated-annealing approach to heuristically optimize a combination of such criteria. Using this method in computational experiments, we explore the trade-offs and dependencies between criteria for computing high-quality schematic set visualizations

PENGARUH PENAMBAHAN LENSA NOZZLE DAN JUMLAH BLADE AIRFOIL TIPE NACA 4415 TERHADAP HASIL DAYA LISTRIK TURBIN ANGIN SUMBU HORISONTAL

Danur Lambang Pristiandaru. PENGARUH PENAMBAHAN LENSA NOZZLE TURBIN ANGIN DAN JUMLAH BLADE AIRFOIL TIPE NACA 4415 TERHADAP HASIL DAYA LISTRIK. Skripsi, Fakultas Keguruan dan Ilmu Pendidikan Universitas Sebelas Maret Surakarta. Januari 2016 Tujuan penelitian ini adalah: (1) Menyelidiki pengaruh jumlah blade pada turbin angin non-twisted blade tipe airfoil NACA 4415 terhadap daya listrik yang dihasilkan. (2) Menyelidiki pengaruh penambahan lensa nozzle pada turbin angin non-twisted blade tipe airfoil NACA 4415 terhadap daya listrik yang dihasilkan turbin angin. (3) Menyelidiki pengaruh bersama (interaksi) antara penambahan lensa nozzle dan jumlah blade terhadap daya listrik yang dihasilkan turbin angin. Penelitian ini menggunakan metode deskriptif kuantitatif. Sampel dalam penelitian ini adalah Turbin Angin Sumbu Horisontal (TASH) dengan desain blade airfoil NACA 4415 non-twisted. 3 desain lensa nozzle digunakan untuk mengetahui pengaruhnya terhadap peningkatan daya listrik TASH. Terdapat 3 variasi jumlah blade yaitu jumlah blade 2, jumlah blade 3, dan jumlah blade 4. Variasi kecepatan angin yang digunakan dalam penelitian ini adalah 2,5 m/s, 3,5 m/s, dan 4,5 m/s. Data diperoleh dengan melakukan pengujian TASH menggunakan angin rekayasa, daya listrik yang dihasilkan dibaca dan direkam oleh data logger. Data yang diperoleh dari hasil penelitian dimasukkan ke dalam tabel dan ditampilkan dalam bentuk grafik, kemudian dianalisis. Berdasarkan hasil penelitian dapat disimpulkan bahwa: (1) Adanya pengaruh variasi jumlah blade terhadap daya listrik turbin angin. TASH 3 blade menghasilkan daya listrik yang paling besar yaitu 0,7222 W pada kecepatan angin 4,5 m/s. (2) Adanya pengaruh penambahan lensa nozzle terhadap turbin angin. Lensa nozzle mampu meningkatkan hasil daya listrik turbin angin semua jenis variasi jumlah blade dibandingkan turbin angin tanpa lensa nozzle. (3) Ada pengaruh bersama yang signifikan antara variasi jumlah blade dan variasi jenis lensa terhadap daya listrik turbin angin. TASH 3 blade dengan lensa C pada kecepatan angin 4,5 m/s memiliki daya listrik tertinggi yaitu sebesar 0,82041 W. Daya listrik tersebut meningkat 13,60% dibanding TASH 3 blade tanpa penambahan lensa, yaitu 0,7222 W. Kata kunci: Turbin Angin, Lensa Nozzle, Daya Listrik, Data Logge

Multi-stack Boundary Labeling Problems

Abstract. The boundary labeling problem was recently introduced in [4] as a response to the problem of labeling dense point sets with large labels. In boundary labeling, we are given a rectangle R which encloses a set of n sites. Each site pi is associated with an axis-parallel rectangular label li. The main task is to place the labels in distinct positions on the boundary of R, so that they do not overlap, and to connect each site with its corresponding label by non-intersecting polygonal lines, so called leaders. Such a label placement is referred to as legal leader-label placement. In this paper, we study boundary labeling problems along a new line of research. We seek to obtain labelings with labels arranged on more than one stacks placed at the same side of the enclosing rectangle R. We refer to problems of this type as multi-stack boundary labeling problems. We present algorithms for maximizing the uniform label size for boundary labeling with two and three stacks of labels. The key component of our algorithms is a technique that combines the merging of lists and the bounding of the search space of the solution. We also present NPhardness results for multi-stack boundary labeling problems with labels of variable height.

Luatodonotes: Boundary Labeling for Annotations in Texts

We present a tool for annotating Latex documents with comments. Our annotations are placed in the left, right, or both margins, and connected to the corresponding positions in the text with arrows (so-called leaders). Problems of this type have been studied under the name boundary labeling. We consider various leader types (straight-line, rectilinear, and Bézier) and modify existing algorithms to allow for annotations of varying height. We have implemented our algorithms in Lua; they are available for download as an easy-to-use Luatex package