The B36/S125 "2x2" Life-Like Cellular Automaton

The B36/S125 (or "2x2") cellular automaton is one that takes place on a 2D square lattice much like Conway's Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but eventually stable evolution and the existence of a natural diagonal glider, the individual objects that the rule contains generally look very different from their Life counterparts. In this article, a history of notable discoveries in the 2x2 rule is provided, and the fundamental patterns of the automaton are described. Some theoretical results are derived along the way, including a proof that the speed limits for diagonal and orthogonal spaceships in this rule are c/3 and c/2, respectively. A Margolus block cellular automaton that 2x2 emulates is investigated, and in particular a family of oscillators made up entirely of 2 x 2 blocks are analyzed and used to show that there exist oscillators with period 2^m(2^k - 1) for any integers m,k \geq 1.Comment: 18 pages, 19 figure

An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure

The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3. This improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and O^*(1.260^n) by Eppstein. Our algorithm is a simple branch-and-search algorithm. The only branch rule is designed on a cut-circuit structure of a graph induced by unprocessed edges. To improve a time bound by a simple analysis on measure and conquer, we introduce an amortization scheme over the cut-circuit structure by defining the measure of an instance to be the sum of not only weights of vertices but also weights of connected components of the induced graph.Comment: 24 pages and 4 figure

Superpatterns and Universal Point Sets

An old open problem in graph drawing asks for the size of a universal point set, a set of points that can be used as vertices for straight-line drawings of all n-vertex planar graphs. We connect this problem to the theory of permutation patterns, where another open problem concerns the size of superpatterns, permutations that contain all patterns of a given size. We generalize superpatterns to classes of permutations determined by forbidden patterns, and we construct superpatterns of size n^2/4 + Theta(n) for the 213-avoiding permutations, half the size of known superpatterns for unconstrained permutations. We use our superpatterns to construct universal point sets of size n^2/4 - Theta(n), smaller than the previous bound by a 9/16 factor. We prove that every proper subclass of the 213-avoiding permutations has superpatterns of size O(n log^O(1) n), which we use to prove that the planar graphs of bounded pathwidth have near-linear universal point sets.Comment: GD 2013 special issue of JGA

Vertex-Unfoldings of Simplicial Polyhedra

We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have a disconnected interior: the triangles are connected at vertices, but not necessarily joined along edges.Comment: 10 pages; 7 figures; 8 reference

All Maximal Independent Sets and Dynamic Dominance for Sparse Graphs

We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per set generated; for minor-closed graph families, the time is O(n) per set, and for more general sparse graph families we achieve subquadratic time per set. We also describe new data structures for maintaining a dynamic vertex set S in a sparse or minor-closed graph family, and querying the number of vertices not dominated by S; for minor-closed graph families the time per update is constant, while it is sublinear for any sparse graph family. We can also maintain a dynamic vertex set in an arbitrary m-edge graph and test the independence of the maintained set in time O(sqrt m) per update. We use the domination data structures as part of our enumeration algorithms.Comment: 10 page

Proximity Drawings of High-Degree Trees

A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of higher degree? We approach this question by supposing that a partition or covering of the tree by subtrees of bounded degree is given. Then we show that if the partition or covering satisfies some natural properties, then there is a drawing of the entire tree such that each of the given subtrees is drawn as a minimum spanning tree of its vertex set

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