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Strongly Connected Orientation
In graph theory, a strong orientation of an undirected graph is an assignment of a direction to each edge (an orientation) that makes it into a strongly connected graph. Strong orientations have been applied to the design of one-way road networks. According to Robbins' theorem, the graphs with strong orientations are exactly the bridgeless graphs. Eulerian orientations and well-balanced orientations provide important special cases of strong orientations; in turn, strong orientations may be generalized to totally cyclic orientations of disconnected graphs. The set of strong orientations of a graph forms a partial cube, with adjacent orientations in this structure differing in the orientation of a single edge. It is possible to find a single orientation in linear time, but it is #P-complete to count the number of strong orientations of a given graph. Application to traffic control introduces the problem of strong orientation with a story about a town, whose streets and intersecti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strong Orientation
In graph theory, a strong orientation of an undirected graph is an assignment of a direction to each edge (an Orientation (graph theory), orientation) that makes it into a strongly connected graph. Strong orientations have been applied to the design of one-way road networks. According to Robbins' theorem, the graphs with strong orientations are exactly the bridge (graph theory), bridgeless graphs. Eulerian orientations and well-balanced orientations provide important special cases of strong orientations; in turn, strong orientations may be generalized to totally cyclic orientations of disconnected graphs. The set of strong orientations of a graph forms a partial cube, with adjacent orientations in this structure differing in the orientation of a single edge. It is possible to find a single orientation in linear time, but it is Sharp-P-complete, #P-complete to count the number of strong orientations of a given graph. Application to traffic control introduces the problem of strong ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bipolar Orientation
In graph theory, a bipolar orientation or ''st''-orientation of an undirected graph is an assignment of a direction to each edge (an orientation) that causes the graph to become a directed acyclic graph with a single source ''s'' and a single sink ''t'', and an ''st''-numbering of the graph is a topological ordering of the resulting directed acyclic graph. Definitions and existence Let ''G'' = (''V'',''E'') be an undirected graph with ''n'' = , ''V'', vertices. An orientation of ''G'' is an assignment of a direction to each edge of ''G'', making it into a directed graph. It is an acyclic orientation if the resulting directed graph has no directed cycles. Every acyclically oriented graph has at least one ''source'' (a vertex with no incoming edges) and at least one ''sink'' (a vertex with no outgoing edges); it is a bipolar orientation if it has exactly one source and exactly one sink. In some situations, ''G'' may be given together with two designated vertic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The American Mathematical Monthly
''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. The editor-in-chief is Vadim Ponomarenko (San Diego State University). The journal gives the Lester R. Ford Award annually to "authors of articles of expository excellence" published in the journal. Editors-in-chief The following persons are or have been editor-in-chief: See also *''Mathematics Magazine'' *''Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Combinatorial Theory
The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applications of combinatorics. ''Series B'' is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and are widely known as ''JCTA'' and ''JCTB''. The journal was founded in 1966 by Frank Harary and Gian-Carlo Rota.They are acknowledged on the journals' title pages and Web sites. SeEditorial board of JCTA Originally there was only one journal, which was split into two parts in 1971 as the field grew rapidly. In 2020, most of the editorial board of ''JCTA'' resigned to form a new, |
Graphs And Combinatorics
''Graphs and Combinatorics'' (ISSN 0911-0119, abbreviated ''Graphs Combin.'') is a peer-reviewed academic journal in graph theory, combinatorics, and discrete geometry published by Springer Japan. Its editor-in-chief is Katsuhiro Ota of Keio University. The journal was first published in 1985. Its founding editor in chief was Hoon Heng Teh of Singapore, the president of the Southeast Asian Mathematics Society, and its managing editor was Jin Akiyama. Originally, it was subtitled "An Asian Journal". In most years since 1999, it has been ranked as a second-quartile journal in discrete mathematics and theoretical computer science by SCImago Journal Rank The SCImago Journal Rank (SJR) indicator is a measure of the prestige of scholarly journals that accounts for both the number of citations received by a journal and the prestige of the journals where the citations come from. Etymology SCImago ..... References {{reflist Academic journals established in 1985 Combinatorics jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Processing Letters
''Information Processing Letters'' is a peer review, peer-reviewed scientific journal in the field of computer science, published by Elsevier. The aim of the journal is to enable fast dissemination of results in the field of Data processing, information processing in the form of short papers. Submissions are limited to nine double-spaced pages. The scope of IPL covers fundamental aspects of information processing and computing. This naturally covers topics in the broadly understood field of theoretical computer science, including algorithms, formal languages and automata, computational complexity, computational logic, distributed and parallel algorithms, computational geometry, learning theory, computational number theory, computational biology, coding theory, theoretical cryptography, and applied discrete mathematics. Generally, submissions in all areas of scientific inquiry are considered, provided that they describe research contributions credibly motivated by applications to com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Treewidth
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest treewidth is 1; the graphs with treewidth 1 are exactly the trees and the forests A forest is an ecosystem characterized by a dense community of trees. Hundreds of definitions of forest are used throughout the world, incorporating factors such as tree density, tree height, land use, legal standing, and ecological functio .... An example of graphs with treewidth at most 2 are the series–parallel graphs. The maximal graphs with treewidth exactly are called '' -trees'', and the graphs with treewidth at most are called '' partial -trees''. Many other well-studied graph families also have bounded treewidth. Treewidth may be formally defined in several equivalent ways: in terms of the size of the largest vertex set in a tree decomposition of the graph, in terms of the size of the largest clique in a chordal completi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fully Polynomial-time Randomized Approximation Scheme
In computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems). A PTAS is an algorithm which takes an instance of an optimization problem and a parameter and produces a solution that is within a factor of being optimal (or for maximization problems). For example, for the Euclidean traveling salesman problem, a PTAS would produce a tour with length at most , with being the length of the shortest tour.Sanjeev Arora, Polynomial-time Approximation Schemes for Euclidean TSP and other Geometric Problems, Journal of the ACM 45(5) 753–782, 1998. The running time of a PTAS is required to be polynomial in the problem size for every fixed ε, but can be different for different ε. Thus an algorithm running in time or even counts as a PTAS. Variants Deterministic A practical problem with PTAS algorithms is that the exponent of the polynomial coul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dense Graph
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often represented by 'roughly equal to' statements. Due to this, the way that density is defined often depends on the context of the problem. The graph density of simple graphs is defined to be the ratio of the number of edges with respect to the maximum possible edges. For undirected simple graphs, the graph density is: :D = \frac = \frac For directed, simple graphs, the maximum possible edges is twice that of undirected graphs (as there are two directions to an edge) so the density is: :D = \frac = \frac where is the number of edges and is the number of vertices in the graph. The maximum number of edges for an undirected graph is = \frac2, so the maximal density is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bipartite Graph
In the mathematics, mathematical field of graph theory, a bipartite graph (or bigraph) is a Graph (discrete mathematics), graph whose vertex (graph theory), vertices can be divided into two disjoint sets, disjoint and Independent set (graph theory), independent sets U and V, that is, every edge (graph theory), edge connects a Vertex (graph theory), vertex in U to one in V. Vertex sets U and V are usually called the ''parts'' of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycle (graph theory), cycles. The two sets U and V may be thought of as a graph coloring, coloring of the graph with two colors: if one colors all nodes in U blue, and all nodes in V red, each edge has endpoints of differing colors, as is required in the graph coloring problem.. In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a Gallery of named graphs, triangle: after one node is colored blue and another red, the third vertex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-complete
In computational complexity theory, NP-complete problems are the hardest of the problems to which ''solutions'' can be verified ''quickly''. Somewhat more precisely, a problem is NP-complete when: # It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". # When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) ''solution''. # The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # The problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. Hence, if we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Time
In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
