Related papers: Testing Upward Planarity of Partial $2$-Trees
In the Connected Vertex Cover problem we are given an undirected graph G together with an integer k and we are to find a subset of vertices X of size at most k, such that X contains at least one end-point of each edge and moreover X induces…
An out-tree $T$ is an oriented tree with only one vertex of in-degree zero. A vertex $x$ of $T$ is internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a…
The Planar Steiner Tree problem is one of the most fundamental NP-complete problems as it models many network design problems. Recall that an instance of this problem consists of a graph with edge weights, and a subset of vertices (often…
In this paper, we give a polynomial-time algorithm for deciding whether an input bipartite graph admits a 2-layer fan-planar drawing, resolving an open problem posed in several papers since 2015.
In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let $G = (V, E)$ be a directed graph and let $\ell: V \to \mathcal P(\mathbb Z)$ be a…
We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, {\sc $k$-Leaf…
In the past thirty years, numerous algorithms for building the suffix array of a string have been proposed. In 2021, the notion of suffix array was extended from strings to DFAs, and it was shown that the resulting data structure can be…
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
We show a new simple algorithm that checks whether a given higher-order grammar generates a nonempty language of trees. The algorithm amounts to a procedure that transforms a grammar of order n to a grammar of order n-1, preserving…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
An out-branching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given directed graph D has an out-branching with at least k leaves (Directed…
We give an $O(n \log^3 n)$ approximation scheme for Steiner forest in planar graphs, improving on the previous approximation scheme for this problem, which runs in $O(n^{f(\epsilon)})$ time.
We give a greedy learning algorithm for reconstructing an evolutionary tree based on a certain harmonic average on triplets of terminal taxa. After the pairwise distances between terminal taxa are estimated from sequence data, the algorithm…
We study the NodeTrix planarity testing problem for flat clustered graphs when the maximum size of each cluster is bounded by a constant $k$. We consider both the case when the sides of the matrices to which the edges are incident are fixed…
We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…
Here, we give an algorithm for deciding if the nonnegative rank of a matrix $M$ of dimension $m \times n$ is at most $r$ which runs in time $(nm)^{O(r^2)}$. This is the first exact algorithm that runs in time singly-exponential in $r$. This…
The {\sc Directed Maximum Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we improve known parameterized algorithms and…
Algorithms are given for determining $L_\infty$ isotonic regression of weighted data. For a linear order, grid in multidimensional space, or tree, of $n$ vertices, optimal algorithms are given, taking $\Theta(n)$ time. These improve upon…
Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and…
We give algorithms to compute the Fr\'echet distance of trees and graphs with bounded tree width. Our algorithms run in $O(n^2)$ time for trees of bounded degree, and $O(n^2\sqrt{n \log n})$ time for trees of arbitrary degree. For graphs of…