Related papers: Reachability in arborescence packings
We give a simple algorithm that determines whether a given post-critically finite topological polynomial is Thurston equivalent to a polynomial. If it is, the algorithm produces the Hubbard tree; otherwise, the algorithm produces the…
Using standard methods (due to Janson, Stein-Chen, and Talagrand) from probabilistic combinatorics, we explore the following general theme: As one progresses from each member of a family of objects ${\cal A}$ being "covered" by at most one…
Given a graph and a root, the Maximum Bounded Rooted-Tree Packing (MBRTP) problem aims at finding K rooted-trees that span the largest subset of vertices, when each vertex has a limited outdegree. This problem is motivated by peer-to-peer…
2D nesting problems rank among the most challenging cutting and packing problems. Yet, despite their practical relevance, research over the past decade has seen remarkably little progress. One reasonable explanation could be that nesting…
Trees with many leaves have applications on broadcasting, which is a method in networks for transferring a message to all recipients simultaneously. Internal nodes of a broadcasting tree require more expensive technology, because they have…
Recently, it was proved by B\'erczi and Schwarcz that the problem of factorizing a matroid into rainbow bases with respect to a given partition of its ground set is algorithmically intractable. On the other hand, many special cases were…
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…
In recent work, Gourv\`es, Lesca, and Wilczynski propose a variant of the classic housing markets model where the matching between agents and objects evolves through Pareto-improving swaps between pairs of adjacent agents in a social…
The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…
Like most multiobjective combinatorial optimization problems, biobjective optimization problems on matroids are in general intractable and their corresponding decision problems are in general NP-hard. In this paper, we consider biobjective…
In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed…
We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher…
We study a constrained shortest path problem in group-labeled graphs with nonnegative edge length, called the shortest non-zero path problem. Depending on the group in question, this problem includes two types of tractable variants in…
The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…
We consider the bin packing problem with $d$ different item sizes and revisit the structure theorem given by Goemans and Rothvo\ss [6] about solutions of the integer cone. We present new techniques on how solutions can be modified and give…
Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent…
Computing supertrees is a central problem in phylogenetics. The supertree method that is by far the most widely used today was introduced in 1992 and is called Matrix Representation with Parsimony analysis (MRP). Matrix Representation using…
We consider the problem of determining whether a target item assignment can be reached from an initial item assignment by a sequence of pairwise exchanges of items between agents. In particular, we consider the situation where each agent…
This paper is devoted to one theory of hypergraph connectivity and presents the proof of the polynomial algorithm for finding an optimal spanning hyperforest(hypertree) for any given weighed q-uniform hypergraph.
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…