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The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its…
We propose an algorithmic framework for efficient anytime motion planning on large dense geometric roadmaps, in domains where collision checks and therefore edge evaluations are computationally expensive. A large dense roadmap (graph) can…
We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions…
Reachability questions are one of the most fundamental algorithmic primitives in temporal graphs -- graphs whose edge set changes over discrete time steps. A core problem here is the NP-hard Short Restless Temporal Path: given a temporal…
Lattice paths are functional entities that model efficient navigation in discrete/grid maps. This paper presents a new scheme to generate collision-free lattice paths with utmost efficiency using the bijective property to rooted ordered…
The crossing number of a graph is the minimum number of edge crossings that a graph can have when drawn in the plane. Determining this number, known as the Crossing Number problem, is a celebrated problem in combinatorial optimization. It…
In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…
In a temporal graph the edge set dynamically changes over time according to a set of time-labels associated with each edge that indicates at which time-steps the edge is available. Two vertices are connected if there is a path connecting…
A path-covering problem on a directed acyclic graph (DAG) requires finding a set of source-to-sink paths that cover all the nodes, all the arcs, or subsets thereof, and additionally they are optimal with respect to some function. In this…
Finding the shortest-path distance between two arbitrary vertices is an important problem in road networks. Due to real-time traffic conditions, road networks undergo dynamic changes all the time. Current state-of-the-art methods…
Interactions between two entities often occur at specific timestamps, which can be modeled as a temporal graph. Exploring the relationships between vertices based on temporal paths is one of the fundamental tasks. In this paper, we conduct…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art…
The dynamic response of power grids to small transient events or persistent stochastic disturbances influences their stable operation. This paper studies the effect of topology on the linear time-invariant dynamics of power networks. For a…
The present paper studies local distributed graph problems in highly dynamic networks. Communication and changes of the graph happen in synchronous rounds and our algorithms always, i.e., in every round, satisfy non-trivial guarantees, no…
Given a graph $G$, the longest path problem asks to compute a simple path of $G$ with the largest number of vertices. This problem is the most natural optimization version of the well known and well studied Hamiltonian path problem, and…
Temporal graphs arise when modeling interactions that evolve over time. They usually come in several flavors, depending on the number of parameters used to describe the temporal aspects of the interactions: time of appearance, duration,…
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…