Céline M. F. Swennenhuis
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View article: Parameterized problems complete for nondeterministic FPT time and logarithmic space
Parameterized problems complete for nondeterministic FPT time and logarithmic space Open
Let XNLP be the class of parameterized problems such that an instance of size n with parameter k can be solved nondeterministically in time f(k)nO(1) and space f(k)log(n) (for some computable function f). We give a wide variety of XNLP-co…
View article: Steiner Tree Parameterized by Multiway Cut and Even Less
Steiner Tree Parameterized by Multiway Cut and Even Less Open
In the Steiner Tree problem we are given an undirected edge-weighted graph as input, along with a set $K$ of vertices called terminals. The task is to output a minimum-weight connected subgraph that spans all the terminals. The famous Drey…
View article: Scheduling jobs that change over time
Scheduling jobs that change over time Open
We consider a 1-machine scheduling problem where the temperature of a job rises during processing, and cools down when not being processed according to given linear heating and cooling rates. No job's temperature is allowed to rise above a…
View article: A Subexponential Time Algorithm for Makespan Scheduling of Unit Jobs with Precedence Constraints
A Subexponential Time Algorithm for Makespan Scheduling of Unit Jobs with Precedence Constraints Open
In a classical scheduling problem, we are given a set of $n$ jobs of unit length along with precedence constraints, and the goal is to find a schedule of these jobs on $m$ identical machines that minimizes the makespan. Using the standard …
View article: Hamiltonian Cycle Parameterized by Treedepth in Single Exponential Time and Polynomial Space
Hamiltonian Cycle Parameterized by Treedepth in Single Exponential Time and Polynomial Space Open
For many algorithmic problems on graphs of treewidth t, a standard dynamic programming approach gives algorithms with time and space complexity 2 (*'-n ' K It turns out that when one considers the more restrictive parameter treedepth, it i…
View article: Parameterized Complexities of Dominating and Independent Set Reconfiguration
Parameterized Complexities of Dominating and Independent Set Reconfiguration Open
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on…
View article: Makespan Scheduling of Unit Jobs with Precedence Constraints in $O(1.995^n)$ time
Makespan Scheduling of Unit Jobs with Precedence Constraints in $O(1.995^n)$ time Open
In a classical scheduling problem, we are given a set of $n$ jobs of unit length along with precedence constraints and the goal is to find a schedule of these jobs on $m$ identical machines that minimizes the makespan. This problem is well…
View article: Isolation Schemes for Problems on Decomposable Graphs
Isolation Schemes for Problems on Decomposable Graphs Open
The Isolation Lemma of Mulmuley, Vazirani and Vazirani [Combinatorica'87] provides a self-reduction scheme that allows one to assume that a given instance of a problem has a unique solution, provided a solution exists at all. Since its int…
View article: Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space
Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space Open
Let XNLP be the class of parameterized problems such that an instance of size n with parameter k can be solved nondeterministically in time $f(k)n^{O(1)}$ and space $f(k)\log(n)$ (for some computable function f). We give a wide variety of …
View article: A Faster Exponential Time Algorithm for Bin Packing With a Constant Number of Bins via Additive Combinatorics
A Faster Exponential Time Algorithm for Bin Packing With a Constant Number of Bins via Additive Combinatorics Open
In the Bin Packing problem one is given $n$ items with weights\n$w_1,\\ldots,w_n$ and $m$ bins with capacities $c_1,\\ldots,c_m$. The goal is to\nfind a partition of the items into sets $S_1,\\ldots,S_m$ such that $w(S_j) \\leq\nc_j$ for e…
View article: Parameterized Complexities of Dominating and Independent Set Reconfiguration
Parameterized Complexities of Dominating and Independent Set Reconfiguration Open
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on…
View article: Hamiltonian Cycle Parameterized by Treedepth in Single Exponential Time and Polynomial Space
Hamiltonian Cycle Parameterized by Treedepth in Single Exponential Time and Polynomial Space Open
For many algorithmic problems on graphs of treewidth $t$, a standard dynamic programming approach gives an algorithm with time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. It turns out that when one considers the more…
View article: Parameterized Complexity of Partial Scheduling
Parameterized Complexity of Partial Scheduling Open
We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, hav…
View article: Parallel Machine Scheduling with a Single Resource per Job
Parallel Machine Scheduling with a Single Resource per Job Open
We study the problem of scheduling jobs on parallel machines minimizing the total completion time, with each job using exactly one resource. First, we derive fundamental properties of the problem and show that the problem is polynomially s…