Related papers: Width, depth and space
We present a dynamic data structure for representing a graph $G$ with tree-depth at most $D$. Tree-depth is an important graph parameter which arose in the study of sparse graph classes. The structure allows addition and removal of edges…
In spite of the extensive studies of the 3-coloring problem with respect to several basic parameters, the complexity status of the 3-coloring problem on graphs with small diameter, i.e. with diameter 2 or 3, has been a longstanding and…
Motivated by the importance of dynamic programming (DP) in parameterized complexity, we consider several fine-grained questions, such as the following examples: (i) can Dominating Set be solved in time $(3-\epsilon)^{pw}n^{O(1)}$? (where…
We present an efficient algorithm to compute permanents, mixed discriminants and hyperdeterminants of structured matrices and multidimensional arrays (tensors). We describe the sparsity structure of an array in terms of a graph, and we…
By a well known result the treewidth of k-outerplanar graphs is at most 3k-1. This paper gives, besides a rigorous proof of this fact, an algorithmic implementation of the proof, i.e. it is shown that, given a k-outerplanar graph G, a tree…
Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays a major role in the theory of sparse graph classes. We show that there exists a constant $C$ such that for every positive integers $a,b$ and a graph…
In this work, we introduce TreeWidzard, an engine for developing dynamic programming algorithms that decide graph-theoretic properties parameterized by treewidth and pathwidth. Besides providing a unified framework for algorithms deciding…
Treewidth is arguably the most important structural graph parameter leading to algorithmically beneficial graph decompositions. Triggered by a strongly growing interest in temporal networks (graphs where edge sets change over time), we…
A connected graph has tree-depth at most $k$ if it is a subgraph of the closure of a rooted tree whose height is at most $k$. We give an algorithm which for a given $n$-vertex graph $G$, in time $\mathcal{O}(1.9602^n)$ computes the…
The Ordered Covering Problem (OCP) arises in the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), where the ordering of pruning edges significantly impacts the performance of the SBBU algorithm for protein structure…
Motivated by a recent result of Elberfeld, Jakoby and Tantau showing that $\mathsf{MSO}$ properties are Logspace computable on graphs of bounded tree-width, we consider the complexity of computing the determinant of the adjacency matrix of…
Graph coloring is one of the central problems in distributed graph algorithms. Much of the research on this topic has focused on coloring with $\Delta+1$ colors, where $\Delta$ denotes the maximum degree. Using $\Delta+1$ colors may be…
This paper settles the computational complexity of model checking of several extensions of the monadic second order (MSO) logic on two classes of graphs: graphs of bounded treewidth and graphs of bounded neighborhood diversity. A classical…
The recent increase of interest in the graph invariant called tree-depth and in its applications in algorithms and logic on graphs led to a natural question: is there an analogously useful "depth" notion also for dense graphs (say; one…
While obtaining optimal algorithms for the most important problems in the LOCAL model has been one of the central goals in the area of distributed algorithms since its infancy, tight complexity bounds are elusive for many problems even when…
Algorithmic meta-theorems, stating that graph properties expressible in some particular logic can be decided efficiently in graph classes having some specific structural properties, are now standard in sequential graph algorithms. One of…
Given a dynamic graph subject to edge insertions and deletions, we show how to update an implicit representation of a proper vertex colouring, such that colours of vertices are computable upon query time. We give a deterministic algorithm…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are "pure" in that they only perform basic operations, as min, max, +, but…
The maximum matching problem in dynamic graphs subject to edge updates (insertions and deletions) has received much attention over the last few years; a multitude of approximation/time tradeoffs were obtained, improving upon the folklore…