Related papers: Solving connectivity problems parameterized by tre…
We consider the problem of enumerating, for a given directed graph $G=(V,E)$ and a node $r\in V$, all directed spanning trees of $G$ rooted at $r$. For undirected graphs, the corresponding problem of enumerating all spanning trees has…
We show fast deterministic algorithms for fundamental problems on forests in the challenging low-space regime of the well-known Massive Parallel Computation (MPC) model. A recent breakthrough result by Coy and Czumaj [STOC'22] shows that,…
We present $k^{O(k^2)} m$ time algorithms for various problems about decomposing a given undirected graph by edge cuts or vertex separators of size $<k$ into parts that are ``well-connected'' with respect to cuts or separators of size $<k$;…
We present a novel algorithm for the minimum-depth elimination tree problem, which is equivalent to the optimal treedepth decomposition problem. Our algorithm makes use of two cheaply-computed lower bound functions to prune the search tree,…
Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…
We give new algorithms for tree evaluation (S. Cook et al. TOCT 2012) in the catalytic-computing model (Buhrman et al. STOC 2014). Two existing approaches aim to solve tree evaluation in low space: on the one hand, J. Cook and Mertz (STOC…
We study the computational complexity of several polynomial-time-solvable graph problems parameterized by vertex integrity, a measure of a graph's vulnerability to vertex removal in terms of connectivity. Vertex integrity is the smallest…
Bounded treewidth is one of the most cited combinatorial invariants, which was applied in the literature for solving several counting problems efficiently. A canonical counting problem is #SAT, which asks to count the satisfying assignments…
In this paper we merge recent developments on exact algorithms for finding an ordering of vertices of a given graph that minimizes bandwidth (the BANDWIDTH problem) and for finding an embedding of a given graph into a line that minimizes…
Many hard graph problems, such as Hamiltonian Cycle, become FPT when parameterized by treewidth, a parameter that is bounded only on sparse graphs. When parameterized by the more general parameter clique-width, Hamiltonian Cycle becomes…
We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…
In this paper, we introduce a novel algorithm to solve projected model counting (PMC). PMC asks to count solutions of a Boolean formula with respect to a given set of projection variables, where multiple solutions that are identical when…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…
Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…
Enumerating the minimal hitting sets of a hypergraph is a problem which arises in many data management applications that include constraint mining, discovering unique column combinations, and enumerating database repairs. Previously, Eiter…
We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that…
For a tree decomposition $\mathcal{T}$ of a graph $G$, by $\mu(\mathcal{T})$ we denote the size of a largest induced matching in $G$ all of whose edges intersect one bag of $\mathcal{T}$. Induced matching treewidth of a graph $G$ is the…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
We prove the following theorem. Given a planar graph $G$ and an integer $k$, it is possible in polynomial time to randomly sample a subset $A$ of vertices of $G$ with the following properties: (i) $A$ induces a subgraph of $G$ of treewidth…
Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…