Related papers: Spectral ordering and 2-switch transformations
We show that reconstructing a tree from order information on triples is NP-hard. This is in contrast to the case for ultra-metrics and for subtree information on quadruples which are both known to allow polynomial time reconstruction.
A "tree-partition" of a graph $G$ is a partition of $V(G)$ such that identifying the vertices in each part gives a tree. It is known that every graph with treewidth $k$ and maximum degree $\Delta$ has a tree-partition with parts of size…
We prove the sufficiency of the Linear Superposition Principle for linear trees, which characterizes the spectra achievable by a real symmetric matrix whose underlying graph is a linear tree. The necessity was previously proven in 2014.…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
We consider the wavelet transform of a finite, rooted, node-ranked, $p$-way tree, focusing on the case of binary ($p = 2$) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through…
We study a sorting machine consisting of two stacks in series where the first stack has the added restriction such that entries in the stack must be in decreasing order from top to bottom. We give the basis of the class of permutations that…
This paper considers Darboux transformations of a bispectral operator which preserve its bispectrality. A sufficient condition for this to occur is given, and applied to the case of generalized Airy operators of arbitrary order $r>1$. As a…
The spectrum of the $k$-power hypergraph of a graph $G$ is called the $k$-ordered spectrum of $G$.If graphs $G_1$ and $G_2$ have same $k$-ordered spectrum for all positive integer $k\geq2$, $G_1$ and $G_2$ are said to be high-ordered…
Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we…
Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…
In this paper we study natural reconfiguration spaces associated to the problem of distributing a fixed number of resources to labeled nodes of a tree network, so that no node is left empty. These spaces turn out to be cubical complexes,…
Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
We consider two different definitions for loop corrections to the primordial power spectra. One of these is to simply correct the mode functions in the tree order relations using the linearized effective field equations. The second…
We discuss transformations on matrices that preserve the effective spectrum and/or the effective spectral radius.
The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree…
We study vertex-ordering problems in loop-free digraphs subject to constraints on the left-going arcs, focusing on existence conditions and computational complexity. As an intriguing special case, we explore vertex-specific lower and upper…
A shelling of a graph, viewed as an abstract simplicial complex that is pure of dimension 1, is an ordering of its edges such that every edge is adjacent to some other edges appeared previously. In this paper, we focus on complete bipartite…
Binary rooted trees, both in the ordered and in the un-ordered case, are well studied structures in the field of combinatorics. The aim of this work is to study particular patterns in these classes of trees. We consider completely…
A tight alignment between the degree vector and the leading eigenvector arises naturally in networks with neutral degree mixing and the absence of local structures. Many real-world networks, however, violate both conditions. We derive…