Related papers: No small nondeterministic read-once branching prog…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

Recently, an interest in constructing pseudorandom or hitting set generators for restricted branching programs has increased, which is motivated by the fundamental issue of derandomizing space-bounded computations. Such constructions have…

We consider uniquely-decodable coding for zero-error network function computation, where in a directed acyclic graph, the single sink node is required to compute with zero error a target function multiple times, whose arguments are the…

We present an explicit pseudorandom generator for oblivious, read-once, permutation branching programs of constant width that can read their input bits in any order. The seed length is $O(\log^2 n)$, where $n$ is the length of the branching…

Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and its complement suffix is minimized. As…

We study the minimum size $f$ of a feedback vertex set in directed and undirected $n$-vertex graphs of given degeneracy or treewidth. In the undirected setting the bound $\frac{k-1}{k+1}n$ is known to be tight for graphs with bounded…

A random binary search tree grown from the uniformly random permutation of $[n]$ is studied. We analyze the exact and asymptotic counts of vertices by rank, the distance from the set of leaves. The asymptotic fraction $c_k$ of vertices of a…

The field of knowledge compilation establishes the tractability of many tasks by studying how to compile them to Boolean circuit classes obeying some requirements such as structuredness, decomposability, and determinism. However, in other…

Given $n$ subspaces of a finite-dimensional vector space over a fixed finite field $\mathbb F$, we wish to find a "branch-decomposition" of these subspaces of width at most $k$ that is a subcubic tree $T$ with $n$ leaves mapped bijectively…

Frick and Grohe [J. ACM 48 (2006), 1184-1206] introduced a notion of graph classes with locally bounded tree-width and established that every first order logic property can be decided in almost linear time in such a graph class. Here, we…

For an undirected tree with $n$ edges labelled by single letters, we consider its substrings, which are labels of the simple paths between pairs of nodes. We prove that there are $O(n^{1.5})$ different palindromic substrings. This solves an…

We show that CSP is fixed-parameter tractable when parameterized by the treewidth of a backdoor into any tractable CSP problem over a finite constraint language. This result combines the two prominent approaches for achieving tractability…

A graph coloring has bounded clustering if each monochromatic component has bounded size. This paper studies such a coloring, where the number of colors depends on an excluded complete bipartite subgraph. This is a much weaker assumption…

The past decade highlighted the usefulness of social network simulations that run on k-regular, n-size, connected graphs. These can be seen as small-scale models of human social networks of large societies. By narrowing down onto k-regular…

For every positive integer $k$, we define the $k$-treedepth as the largest graph parameter $\mathrm{td}_k$ satisfying (i) $\mathrm{td}_k(\emptyset)=0$; (ii) $\mathrm{td}_k(G) \leq 1+ \mathrm{td}_k(G-u)$ for every graph $G$ and every vertex…

The scramble number of a graph provides a lower bound for gonality and an upper bound for treewidth, making it a graph invariant of interest. In this paper we study graphs of scramble number at most two, and give a classification of all…

A decision list is an ordered list of rules. Each rule is specified by a term, which is a conjunction of literals, and a value. Given an input, the output of a decision list is the value corresponding to the first rule whose term is…

Regular word grammars are restricted context-free grammars that define all the recognizable languages of words. This paper generalizes regular grammars from words to certain classes of graphs, by defining regular grammars for unordered…

Recently, considerable focus has been given to the problem of determining the boundary between tractable and intractable planning problems. In this paper, we study the complexity of planning in the class C_n of planning problems,…

One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic is fixed-parameter tractable on C by linear time parameterised algorithms. An immediate…