The Complexity of Ultrametric Partitions on Graphs
نویسنده
چکیده
Partitioning of graphs has many practical applications namely in cluster analysis and in automated design of VLSI circuits. Using l-l correspondence between ultrametric partitions of a weighted complete graph K(w) on a finite set X and ultrametrics on X, the computational complexity of the approximation of w by means of an ultrametric u is investigated and systematized. As a main result. a polynomial algorithm that solves the problem under some ‘min-max’ criterion is developed.
منابع مشابه
k-Efficient partitions of graphs
A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
متن کاملPlanar Ultrametric Rounding for Image Segmentation
We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect matching as a subroutine in order to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentat...
متن کاملOn Symbolic Ultrametrics, Cotree Representations, and Cograph Edge Decompositions and Partitions
Symbolic ultrametrics define edge-colored complete graphs Kn and yield a simple tree representation of Kn. We discuss, under which conditions this idea can be generalized to find a symbolic ultrametric that, in addition, distinguishes between edges and non-edges of arbitrary graphs G = (V,E) and thus, yielding a simple tree representation of G. We prove that such a symbolic ultrametric can only...
متن کاملPlanar Ultrametrics for Image Segmentation
We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of finding the closest ultrametric to a specified set of distances and solve it using an LP relaxation that leverages minimum cost perfect matching as a subroutine to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentation.
متن کاملList Partitions of Chordal Graphs
In an earlier paper we gave efficient algorithms for partitioning chordal graphs into k independent sets and l cliques. This is a natural generalization of the problem of recognizing split graphs, and is NPcomplete for graphs in general, unless k ≤ 2 and l ≤ 2. (Split graphs have k = l = 1.) In this paper we expand our focus and consider generalM -partitions, also known as trigraph homomorphism...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Inf. Process. Lett.
دوره 27 شماره
صفحات -
تاریخ انتشار 1988