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George, J. Alan (1977), "Solution of linear systems of equations: direct methods for finite element problems",
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The partition of a graph into its level structure may be used as a heuristic for graph layout problems such as
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either has both of its endpoints within the same level, or its two endpoints are in consecutive levels.
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An example for an undirected Graph with a vertex r and its corresponding level structure
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is a refinement of this idea, based on an additional sorting step within each level.
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Sparse matrix techniques (Adv. Course, Technical Univ. Denmark, Copenhagen, 1976)
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350:; McKee, J. (1969), "Reducing the bandwidth of sparse symmetric matrices",
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385:, Berlin: Springer, pp. 52â101. Lecture Notes in Math., Vol. 572,
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101:, the level structure is a partition of the vertices into subsets
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The level structure of a graph can be computed by a variant of
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v is not yet marked: add v to Q'
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mark all vertices in Q as discovered Q' â {}
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to be the set of vertices that are neighbors to vertices in
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Proceedings of the 1969 24th national conference (ACM '69)
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called levels, consisting of the vertices at distance
116:. Equivalently, this set may be defined by setting
411:(1979), "A separator theorem for planar graphs",
330:Algorithms and Data Structures: The Basic Toolbox
232:Level structures are also used in algorithms for
148:but are not themselves in any earlier level.
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24:For the concept in algebraic geometry, see
175:// the set Q holds all vertices at level â
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26:level structure (algebraic geometry)
413:SIAM Journal on Applied Mathematics
270:"A survey of graph layout problems"
209:In a level structure, each edge of
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161:level-BFS(G, r): Q â {r}
54:into subsets that have the same
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189:edge (u, v):
131: > 0, defining
264:DĂaz, Josep; Petit, Jordi;
238:separators of planar graphs
62:Definition and construction
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173:â: process(Q, â)
58:from a given root vertex.
23:
354:, ACM, pp. 157â172,
197:Q' is empty:
97:, and with a root vertex
236:, and for constructing
227:CuthillâMcKee algorithm
21:
360:10.1145/800195.805928
299:10.1145/568522.568523
277:ACM Computing Surveys
19:
455:Graph theory objects
153:breadth-first search
146: − 1
405:Lipton, Richard J.
22:
409:Tarjan, Robert E.
127:}, and then, for
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223:graph bandwidth
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68:connected graph
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419:(2): 177â189,
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325:Sanders, Peter
321:Mehlhorn, Kurt
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290:10.1.1.12.4358
283:(3): 313â356,
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266:Serna, Maria
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217:Applications
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85:the set of
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36:graph theory
34:subfield of
32:mathematical
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348:Cuthill, E.
336:. Springer.
93:the set of
244:References
205:Properties
421:CiteSeerX
285:CiteSeerX
159:algorithm
48:partition
449:Category
368:18143635
327:(2008).
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268:(2002),
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