Simultaneous Embeddability of Two Partitions
نویسندگان
چکیده
We study the simultaneous embeddability of a pair of partitions of the same underlying set into disjoint blocks. Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region that contains exactly those points that belong to the elements in the block and that is bounded by a simple closed curve. We establish three main classes of simultaneous embeddability (weak, strong, and full embeddability) that differ by increasingly strict well-formedness conditions on how different block regions are allowed to intersect. We show that these simultaneous embeddability classes are closely related to different planarity concepts of hypergraphs. For each embeddability class we give a full characterization. We show that (i) every pair of partitions has a weak simultaneous embedding, (ii) it is NP-complete to decide the existence of a strong simultaneous embedding, and (iii) the existence of a full simultaneous embedding can be tested in linear time.
منابع مشابه
On stable embeddability of partitions
Several natural partial orders on integral partitions, such as the embeddability, the stable embeddability, the bulk embeddability and the supermajorization, raise in the quantum computation, bin-packing and matrix analysis. We find the implications between these partial orders. For integral partitions whose entries are all powers of a fixed number p, we show that the embeddability is completel...
متن کاملSimultaneous Visualization of Clusterings
While there are a number of approaches for the visualization of hierarchical clusterings, as well as subsets in general, there exist only few attempts to visualize different clusterings simultaneously in the same drawing. In this thesis we lay the theoretical foundations for the simultaneous visualization of two or more clusterings. We establish a class-hierarchy that allows us to characterize ...
متن کاملTsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions
The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...
متن کاملCFD analysis of natural convection heat transfer in a square cavity with partitions utilizing Al2O3 nanofluid
In the present study, natural convective heat transfer in a partitioned square cavity utilizing nanofluids is studied. The vertical left and right walls are considered as the hot and cold walls, respectively and the partitions assumed to be adiabatic. The nanofluid used in this study is Al2O3 with the volume fraction of 20%. It is assumed that nanofluid is a single phase f...
متن کاملModelling simultaneous broadcasting by level-disjoint partitions
Simultaneous broadcasting of multiple messages from the same source vertex in synchronous networks is considered under restrictions that each vertex receives at most one message in a unit time step, every received message can be sent out only in the next time step, no message is sent to already informed vertex. The number of outgoing messages in unrestricted, messages have unit length, and we a...
متن کامل