Preprocessing (data reduction or kernelization) to reduce instance size is one of the most commonly deployed heuristics in the implementation practice to tackle computationally hard problems. However, a systematic theoretical study of them remained elusive so far. One of the reasons for this is that if an input to an NP -hard problem can be processed in polynomial time to an equivalent one of s...

We study the fixed-parameter tractability, subexponential time computability, and approximability of the well-known NP-hard problems: INDEPENDENT SET, VERTEX COVER, and DOMINATING SET. We derive tight results and show that the computational complexity of these problems, with respect to the above complexity measures, is dependent on the genus of the underlying graph. For instance, we show that, ...

In this paper we study the problem of finding an induced subgraph of size at most k with minimum degree at least d for a given graph G, from the parameterized complexity perspective. We call this problem Minimum Subgraph of Minimum Degree ≥d (MSMDd). For d = 2 it corresponds to finding a shortest cycle of the graph. Our main motivation to study this problem is its strong relation to Dense k-Sub...

Recently, the problem of counting Hamiltonian cycles in 2-tiled graphs was resolved by Vegi Kalamar, Bokal, and Žerak. In this paper, we continue our research on generalized tiled graphs. We extend algorithms traversing from to further show that, similarly as for graphs, a fixed finite set tiles, can be performed linear time with respect size such graph, implying that is fixed-parameter tractab...

The NP-hard k-Anonymity problem asks, given an n×mmatrix M over a fixed alphabet and an integer s > 0, whether M can be made k-anonymous by suppressing (blanking out) at most s entries. A matrix M is said to be k-anonymous if for each row r in M there are at least k − 1 other rows in M which are identical to r. Complementing previous work, we introduce two new “data-driven” parameterizations fo...

Fixed-parameter tractability Definition 2. A parameterized problem Π is fixed-parameter tractable (FPT) if there is an algorithm solving Π in time f(k) · poly(n), where n is the instance size, k is the parameter, poly is a polynomial function, and f is a computable function. Theorem 3. Let Π be a decidable parameterized problem. Π has a kernelization ⇔ Π is FPT. 2 A kernel for Hamiltonian Cycle...

The workflow satisfiability problem is concerned with determining whether it is possible to find an allocation of authorized users to the steps in a workflow in such a way that all constraints are satisfied. The problem is NP-hard in general, but is known to be fixed-parameter tractable for certain classes of constraints. The known results on fixed-parameter tractability rely on the symmetry (i...

In this paper, we continue the study of computational complexity aspects of Seidel’s switching, concentrating on Fixed Parameter Complexity. Among other results we show that switching to a graph with at most k edges, to a graph of maximum degree at most k, to a k-regular graph, or to a graph with minimum degree at least k are fixed parameter tractable problems, where k is the parameter. On the ...

We study the boundary of tractability for the Max-Cut problem in graphs. Our main result shows that Max-Cut above the EdwardsErdős bound is fixed-parameter tractable: we give an algorithm that for any connected graph with n vertices and m edges finds a cut of size

We give a simple and intuitive fixed parameter tractable algorithm for the Odd Cycle Transversal problem, running in time O(3 · k · |E| · |V |). Our algorithm is best viewed as a reinterpretation of the classical Iterative Compression algorithm for Odd Cycle Transversal by Reed, Smith and Vetta [8].