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The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly once. The problem may specify the start and end of the path, in which case the starting vertex s and ending vertex t must be identified.
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In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set of vertices such that for every two vertices in , there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in . A set is independent if and only if it is a clique in the graph's complement. The size of an independent set is the number of vertices it contains. Independent sets have also been called "internally stable sets", of which "stable set" is a shortening.
In graph theory, a vertex cover of a graph is a set of vertices that includes at least one endpoint of every edge of the graph.
Jack Joseph Dongarra is an American computer scientist and mathematician. He is the American University Distinguished Professor of Computer Science in the Electrical Engineering and Computer Science Department at the University of Tennessee. He holds the position of a Distinguished Research Staff member in the Computer Science and Mathematics Division at Oak Ridge National Laboratory, Turing Fellowship in the School of Mathematics at the University of Manchester, and is an adjunct professor and teacher in the Computer Science Department at Rice University. He served as a faculty fellow at the Texas A&M University Institute for Advanced Study (2014–2018). Dongarra is the founding director of the Innovative Computing Laboratory at the University of Tennessee. He was the recipient of the Turing Award in 2021.
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Maximum cardinality matching is a fundamental problem in graph theory. We are given a graph G, and the goal is to find a matching containing as many edges as possible; that is, a maximum cardinality subset of the edges such that each vertex is adjacent to at most one edge of the subset. As each edge will cover exactly two vertices, this problem is equivalent to the task of finding a matching that covers as many vertices as possible.
Search-based software engineering (SBSE) applies metaheuristic search techniques such as genetic algorithms, simulated annealing and tabu search to software engineering problems. Many activities in software engineering can be stated as optimization problems. Optimization techniques of operations research such as linear programming or dynamic programming are often impractical for large scale software engineering problems because of their computational complexity or their assumptions on the problem structure. Researchers and practitioners use metaheuristic search techniques, which impose little assumptions on the problem structure, to find near-optimal or "good-enough" solutions.
In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification over sets. It is particularly important in the logic of graphs, because of Courcelle's theorem, which provides algorithms for evaluating monadic second-order formulas over graphs of bounded treewidth. It is also of fundamental importance in automata theory, where the Büchi–Elgot–Trakhtenbrot theorem gives a logical characterization of the regular languages.
In theoretical computer science, Baker's technique is a method for designing polynomial-time approximation schemes (PTASs) for problems on planar graphs. It is named after Brenda Baker, who announced it in a 1983 conference and published it in the Journal of the ACM in 1994.
In geometry, a covering of a polygon is a set of primitive units whose union equals the polygon. A polygon covering problem is a problem of finding a covering with a smallest number of units for a given polygon. This is an important class of problems in computational geometry. There are many different polygon covering problems, depending on the type of polygon being covered. An example polygon covering problem is: given a rectilinear polygon, find a smallest set of squares whose union equals the polygon.
Philip N. Klein is an American computer scientist and professor at Brown University. His research focuses on algorithms for optimization problems in graphs.
The mixed Chinese postman problem (MCPP or MCP) is the search for the shortest traversal of a graph with a set of vertices V, a set of undirected edges E with positive rational weights, and a set of directed arcs A with positive rational weights that covers each edge or arc at least once at minimal cost. The problem has been proven to be NP-complete by Papadimitriou. The mixed Chinese postman problem often arises in arc routing problems such as snow ploughing, where some streets are too narrow to traverse in both directions while other streets are bidirectional and can be plowed in both directions. It is easy to check if a mixed graph has a postman tour of any size by verifying if the graph is strongly connected. The problem is NP hard if we restrict the postman tour to traverse each arc exactly once or if we restrict it to traverse each edge exactly once, as proved by Zaragoza Martinez.
References
- 1 2 Braun, Bob (May 18, 2003), "A matter of mind", The Star-Ledger .
- ↑ Brenda Baker at the Mathematics Genealogy Project
- 1 2 Baker, Brenda S. (2007), IEEE Xplore Author Information , retrieved 2020-05-24
- ↑ Baker, Brenda S. (2011), Professional Background , retrieved 2016-03-19.
- ↑ Grosse, Roger (2011), About me , retrieved 2016-03-19.
- ↑ Baker, Brenda S. (2011), String Pattern Matching and Tools for Analyzing Code , retrieved 2020-05-24
