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We investigate computational problems involving large weights through the lens of kernelization, which is a framework of polynomial-time preprocessing aimed at compressing the instance size. Our main focus is the weighted Clique problem,…
The complexity of problems involving global constraints is usually much more difficult to understand than the complexity of problems only involving local constraints. A natural form of global constraints are connectivity constraints. We…
We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can…
The binary Constraint Satisfaction Problem (CSP) is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables. A binary CSP instance can be presented as a labelled…
One of the most important algorithmic meta-theorems is a famous result by Courcelle, which states that any graph problem definable in monadic second-order logic with edge-set quantifications (i.e., MSO2 model-checking) is decidable in…
We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…
We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and…
This paper studies the problem of, given the structure of a linear-time invariant system and a set of possible inputs, finding the smallest subset of input vectors that ensures system's structural controllability. We refer to this problem…
Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class ${\cal G}$ is bounded by a constant, a wide range of problems that are NP-complete in general…
We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity on the congested clique with about $N^{1/2}$ nodes, where $N$ is the input size. We show…
We consider the fine-grained complexity of sparse graph problems that currently have $\tilde{O}(mn)$ time algorithms, where m is the number of edges and n is the number of vertices in the input graph. This class includes several important…
Structural measures of graphs, such as treewidth, are central tools in computational complexity resulting in efficient algorithms when exploiting the parameter. It is even known that modern SAT solvers work efficiently on instances of small…
We investigate the size complexity of proofs in $Res(s)$ -- an extension of Resolution working on $s$-DNFs instead of clauses -- for families of contradictions given in the {\em unusual binary} encoding. A motivation of our work is size…
Fine-grained reductions have established equivalences between many core problems with $\tilde{O}(n^3)$-time algorithms on $n$-node weighted graphs, such as Shortest Cycle, All-Pairs Shortest Paths (APSP), Radius, Replacement Paths, Second…
Recently, Hegerfeld and Kratsch [ESA 2023] obtained the first tight algorithmic results for hard connectivity problems parameterized by clique-width. Concretely, they gave one-sided error Monte-Carlo algorithms that given a…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…
Clique-width is a well-known graph parameter. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded clique-width. The same holds for NLC-width. In this paper we study the behavior of clique-width…
Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…
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…
A large number of NP-hard graph problems become polynomial-time solvable on graph classes where the mim-width is bounded and quickly computable. Hence, when solving such problems on special graph classes, it is helpful to know whether the…