Related papers: On the Complexity of Solution Extension of Optimiz…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
The complexity of a computational problem is traditionally quantified based on the hardness of its worst case. This approach has many advantages and has led to a deep and beautiful theory. However, from the practical perspective, this…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is…
The power dominating set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes $S$ that power dominates all the nodes, where a node $v$ is power dominated if (1) $v$ is in $S$…
We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
Many distributed optimization algorithms achieve existentially-optimal running times, meaning that there exists some pathological worst-case topology on which no algorithm can do better. Still, most networks of interest allow for…
In recent years, the expander decomposition method was used to develop many graph algorithms, resulting in major improvements to longstanding complexity barriers. This powerful hammer has led the community to (1) believe that most problems…
Genetic Algorithms have established their capability for solving many complex optimization problems. Even as good solutions are produced, the user's understanding of a problem is not necessarily improved, which can lead to a lack of…
Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…
When applying optimization method to a real-world problem, the possession of prior knowledge and preliminary analysis on the landscape of a global optimization problem can give us an insight into the complexity of the problem. This…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible…