M. J. Dinneen. VLSI Layouts and DNA physical mappings. Technical report, Los Alamos National Laboratory, 1996. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
The Proper Interval Colored Graph problem for caterpillar trees - Alvarez, Serna (Correct)
....between intervalizing problems and graph layout problems. The Interval graph completion problem is equivalent to the Profile minimization problem [KC94] also called the MinSumCut problem [DGPT91] Moreover, the Interval colored graph problem is equivalent to the Colored vertex separation [Din96, ADS98b]. In this paper we define another graph layout problem the Proper colored layout problem (pclp) Although the pclp is not equivalent to the picg, by transforming the input graph we will establish a close relationship between both problems. The final result is that the pigc is NP complete for ....
....of (G; Proper Colored Layout Problem (pclp) Given a k colored graph (G; decide whether there is a proper colored layout of (G; G 1 b b b a G 2 X b b b a Figure 1: Some graphs Figure 2: A graph G and a decoration of G. It is known that the clp problem is identical to the icg problem [Din96, ADS98b]. For the proper case this result does not hold. For example, the graph G 1 , given in figure 1, has a proper colored layout, but does not have any proper intervalization (a label inside a circle indicates a color, while a label outside a circle, if any, indicates a node name) However, we will ....
M. J. Dinneen. VLSI Layouts and DNA physical mappings. Technical report, Los Alamos National Laboratory, 1996.
Intervalizing colored graphs is NP-complete for.. - Alvarez, Diaz, Serna (1998) (Correct)
....they construct graphs with pathwidth 2, but not trees. The caterpillars with hairs of length at most 2 are trees with pathwidth 2. To obtain the result, we exploit the relationship between the ICG problem and a layout problem, the Colored Vertex Separation. Both problems were shown identical in [Din96]. The non colored version of the vertex separation problem is an NP Complete problem with several applications in Computer Science (VLSI design, compiler construction, etc. and it has been well studied [Len81, EST79, KP86, Kin92] In section 2 we introduce the basic definitions and the formal ....
....) Let us consider the following problem: Given a k colored graph G = V; E; the colored vertex separation problem (CVS) is to decide if there is a colored layout of G, such that vs(G; k. It is known that for a given parameter k 2 N, the CVS problem is identical to the ICG problem [Din96]. Therefore all the P and NP Completeness results described above for the ICG also apply to the CVS problem. From the definition of colored layout, given a k colored graph G = V; E; if there is a colored layout of G : V Gamma f1; ng, then for all u; v; x 2 V , such that (u) ....
M.J. Dinneen. VLSI Layouts and DNA physical mappings. Technical report, Los Alamos National Laboratory, 1996.
The Hardness of Intervalizing Four Colored Caterpillars - Àlvarez, Díaz, Serna (1998) (Correct)
....of the ICG problem to this case. Actually the constructed graph is a four colored caterpillar with unbounded hair length. To obtain the results, we give a reduction from the multiprocessor scheduling problem to the Colored Vertex Separation problem, a layout formulation of the ICG problem [Din96]. 2 Definitions and basic results A k coloring of a graph G = V; E) is a mapping : V Gamma f1; kg. For any vertex subset V 0 V , let (V 0 ) f(v) j v 2 V 0 g. A proper coloring of G is a coloring such that no two adjacent vertices have the same color. A k colored graph is a ....
....neighbors of u appear) Let us consider the following layout problem: Given a k colored graph G = V; E; the colored vertex separation problem (CVS) is to decide if there is a colored layout of G. It is known that for a given parameter k 2 N, the CVS problem is identical to the ICG problem [Din96]. Therefore all the P and NP Completeness results described above for the ICG problem also apply to the CVS problem. Notice that if a k colored graph has a colored layout then its vertex separation is at most k Gamma 1, and viceversa any graph with vertex separation at most k Gamma 1 can be ....
M.J. Dinneen. VLSI Layouts and DNA physical mappings. Technical report, Los Alamos National Laboratory, 1996.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC