Related papers: Parameterized Algorithms for Computing Pareto Sets
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
A large number of NP-hard graph problems can be solved in $f(w)n^{O(1)}$ time and space when the input graph is provided together with a tree decomposition of width $w$, in many cases with a modest exponential dependence $f(w)$ on $w$.…
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…
This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to…
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…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
Bilevel optimization problems comprise an upper level optimization task that contains a lower level optimization task as a constraint. While there is a significant and growing literature devoted to solving bilevel problems with single…
In this paper, we propose a simple global optimisation algorithm inspired by Pareto's principle. This algorithm samples most of its solutions within prominent search domains and is equipped with a self-adaptive mechanism to control the…
In the past decade, many parameterized algorithms were developed for packing problems. Our goal is to obtain tradeoffs that improve the running times of these algorithms at the cost of computing approximate solutions. Consider a packing…
We study connectivity problems from a fine-grained parameterized perspective. Cygan et al. (TALG 2022) obtained algorithms with single-exponential running time $\alpha^{tw} n^{O(1)}$ for connectivity problems parameterized by treewidth…
Treewidth is a measure of how tree-like a graph is. It has many important algorithmic applications because many NP-hard problems on general graphs become tractable when restricted to graphs of bounded treewidth. Algorithms for problems on…
In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…
A resolving set $S$ of a graph $G$ is a subset of its vertices such that no two vertices of $G$ have the same distance vector to $S$. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a…
We revisit the issue of low-distortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective.Let $M=M(G)$ be the shortest path metric of an edge…
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points,…
An algorithm is presented that solves the Minimum Dominating Set problem exactly using polynomial space based on dynamic programming for a tree decomposition. A direct application of dynamic programming based on a tree decomposition would…
Multi-objective optimization is key to solving many Engineering Design problems, where design parameters are optimized for several performance indicators. However, optimization results are highly dependent on how the designs are…
In this paper we study a scheduling problem arising from executing numerical simulations on HPC architectures. With a constant number of parallel machines, the objective is to minimize the makespan under memory constraints for the machines.…
In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems considering subsets of the objective functions. If the…
We introduce a novel multivariate approach for solving weighted parameterized problems. In our model, given an instance of size $n$ of a minimization (maximization) problem, and a parameter $W \geq 1$, we seek a solution of weight at most…