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Yen's Algorithm
In graph theory, Yen's algorithm computes single-source k shortest path routing, ''K''-shortest loopless paths for a Graph (discrete mathematics), graph with non-negative Glossary of graph theory#Basics, edge cost. The algorithm was published by Jin Y. Yen in 1971 and employs any shortest path algorithm to find the best path, then proceeds to find ''K'' − 1 deviations of the best path. Algorithm Terminology and notation Description The algorithm can be broken down into two parts: determining the first K shortest path routing, k-shortest path, A^1, and then determining all other ''k''-shortest paths. It is assumed that the container A will hold the ''k''-shortest path, whereas the container B will hold the potential ''k''-shortest paths. To determine A^1, the shortest path from the source to the sink, any efficient shortest path algorithm can be used. To find the A^k, where k ranges from 2 to K, the algorithm assumes that all paths from A^1 to A^ have previously ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
K Shortest Path Routing
The ''k'' shortest path routing problem is a generalization of the shortest path routing problem in a given network. It asks not only about a shortest path but also about next ''k−1'' shortest paths (which may be longer than the shortest path). A variation of the problem is the loopless ''k'' shortest paths. Finding ''k'' shortest paths is possible by extending Dijkstra's algorithm or the Bellman-Ford algorithm. History Since 1957, many papers have been published on the ''k'' shortest path routing problem. Most of the fundamental works were done between 1960s and 2001. Since then, most of the research has been on the problem's applications and its variants. In 2010, Michael Günther et al. published a book on ''Symbolic calculation of ''k''-shortest paths and related measures with the stochastic process algebra tool CASPA''. Algorithm Dijkstra's algorithm can be generalized to find the ''k'' shortest paths. Variations There are two main variations of the ''k'' sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Graph (discrete Mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a Set (mathematics), set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then this graph is directed, because owing mon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Glossary Of Graph Theory
This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges. Symbols A B C D E F G H I J K L M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Shortest Path Algorithm
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length or distance of each segment. Definition The shortest path problem can be defined for graphs whether undirected, directed, or mixed. The definition for undirected graphs states that every edge can be traversed in either direction. Directed graphs require that consecutive vertices be connected by an appropriate directed edge. Two vertices are adjacent when they are both incident to a common edge. A path in an undirected graph is a sequence of vertices P = ( v_1, v_2, \ldots, v_n ) \in V \times V \times \cdots \times V such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
K Shortest Path Routing
The ''k'' shortest path routing problem is a generalization of the shortest path routing problem in a given network. It asks not only about a shortest path but also about next ''k−1'' shortest paths (which may be longer than the shortest path). A variation of the problem is the loopless ''k'' shortest paths. Finding ''k'' shortest paths is possible by extending Dijkstra's algorithm or the Bellman-Ford algorithm. History Since 1957, many papers have been published on the ''k'' shortest path routing problem. Most of the fundamental works were done between 1960s and 2001. Since then, most of the research has been on the problem's applications and its variants. In 2010, Michael Günther et al. published a book on ''Symbolic calculation of ''k''-shortest paths and related measures with the stochastic process algebra tool CASPA''. Algorithm Dijkstra's algorithm can be generalized to find the ''k'' shortest paths. Variations There are two main variations of the ''k'' sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dijkstra Algorithm
Dijkstra's algorithm ( ) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. Dijkstra's algorithm finds the shortest path from a given source node to every other node. It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of edges represent the distances between pairs of cities connected by a direct road, then Dijkstra's algorithm can be used to find the shortest route between one city and all other cities. A common application of shortest path algorithms is network routing protocols, most notably IS-IS (Intermediate System to Intermediate System) and OSPF (Open Shortest Path First). It is also employed as a subroutine in al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
