相关论文: The polynomial algorithm for optimal spanning hype…
We present an algorithm for computing a maximum agreement subtree of two unrooted evolutionary trees. It takes O(n^{1.5} log n) time for trees with unbounded degrees, matching the best known time complexity for the rooted case. Our…
We propose a reinforcement-learning algorithm to tackle the challenge of reconstructing phylogenetic trees. The search for the tree that best describes the data is algorithmically challenging, thus all current algorithms for phylogeny…
We prove that a polynomial fraction of the set of $k$-component forests in the $m \times n$ grid graph have equal numbers of vertices in each component, for any constant $k$. This resolves a conjecture of Charikar, Liu, Liu, and Vuong, and…
Let $G$ be a graph on $n$ vertices. For $i\in \{0,1\}$ and a connected graph $G$, a spanning forest $F$ of $G$ is called an $i$-perfect forest if every tree in $F$ is an induced subgraph of $G$ and exactly $i$ vertices of $F$ have even…
We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
We study the query complexity of determining if a graph is connected with global queries. The first model we look at is matrix-vector multiplication queries to the adjacency matrix. Here, for an $n$-vertex graph with adjacency matrix $A$,…
This paper discusses the enumeration for the total number of all rooted spanning forests of the labeled complete tripartite graph. We enumerate the total number by a combinatorial decomposition.
The Hausdorff distance is a relatively new measure of similarity of graphs. The notion of the Hausdorff distance considers a special kind of a common subgraph of the compared graphs and depends on the structural properties outside of the…
Complex real-world optimization problems often involve both discrete decisions and nonlinear relationships between variables. Many such problems can be modeled as polynomial-objective integer programs, encompassing cases with quadratic and…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
In this paper algebraic and combinatorial properties and a computation of the number of the spanning trees are developed for certain graphs. To this purpose, an original method, independent of the spectrum of the Laplacian matrix associated…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
We present a simple linear-time algorithm that finds a spanning tree $T$ of a given $2$-edge-connected graph $G$ such that each vertex $v$ of $T$ has degree at most $\lceil \frac{\deg_G(v)}{2}\rceil + 1$.
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing…
Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and…
The problem of computing all maximal induced subgraphs of a graph G that have a graph property P, also called the maximal P-subgraphs problem, is considered. This problem is studied for hereditary, connected-hereditary and rooted-hereditary…
In this paper, we study the graph polynomial that counts spanning rooted forests f_g of a given graph. This polynomial has a remarkable reciprocity property. We give a new bijective proof for this theorem which has Prufer coding as a…
A recent work shows how we can optimize a tree based mode of operation for a rate 1 hash function. In particular, an algorithm and a theorem are presented for selecting a good tree topology in order to optimize both the running time and the…