Related papers: Orienteering (with Time Windows) on Restricted Gra…
Among the most important variants of the traveling salesman problem (TSP) are those relaxing the constraint that every locus should necessarily get visited, rather taking into account a revenue (prize) for visiting customers. In the…
We consider the problem of finding a Hamiltonian path or a Hamiltonian cycle with precedence constraints in the form of a partial order on the vertex set. We show that the path problem is $\mathsf{NP}$-complete for graphs of pathwidth 4…
We develop an approach for solving rooted orienteering problems with category constraints as found in tourist trip planning and logistics. It is based on expanding partial solutions in a systematic way, prioritizing promising ones, which…
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…
When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example one could decide whether a Hamiltonian path exists for a fixed starting…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
In this paper we consider the problem of connected edge searching of weighted trees. It is shown that there exists a polynomial-time algorithm for finding optimal connected search strategy for bounded degree trees with arbitrary weights on…
We study the knapsack problem with graph theoretic constraints. That is, we assume that there exists a graph structure on the set of items of knapsack and the solution also needs to satisfy certain graph theoretic properties on top of…
In the Travelling Salesman Problem, every vertex of an edge-weighted graph has to be visited by an agent who traverses the edges of the graph. In this problem, it is usually assumed that the costs of each edge are given in advance, making…
Recently, several studies have explored the use of neural network to solve different routing problems, which is an auspicious direction. These studies usually design an encoder-decoder based framework that uses encoder embeddings of nodes…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
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…
Given a graph, when can we orient the edges to satisfy local constraints at the vertices, where each vertex specifies which local orientations of its incident edges are allowed? This family of graph orientation problems is a special kind of…
We consider the problem of listing all spanning trees of a graph $G$ such that successive trees differ by pivoting a single edge around a vertex. Such a listing is called a "pivot Gray code", and it has more stringent conditions than known…
Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…
Color-constrained subgraph problems are those where we are given an edge-colored (directed or undirected) graph and the task is to find a specific type of subgraph, like a spanning tree, an arborescence, a single-source shortest path tree,…
Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. The expanding search problem asks for a search sequence of the vertices so as to minimize the expected time for…
In the Time-Windows Unsplittable Flow on a Path problem (twUFP) we are given a resource whose available amount changes over a given time interval (modeled as the edge-capacities of a given path $G$) and a collection of tasks. Each task is…
Interdiction problems are leader-follower games in which the leader is allowed to delete a certain number of edges from the graph in order to maximally impede the follower, who is trying to solve an optimization problem on the impeded…
We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…