Related papers: A Subexponential Algorithm for ARRIVAL
In railway operations, a timetable is established to determine the departure and arrival times for the trains or other rolling stock at the different stations or relevant points inside the rail network or a subset of this network. The…
This paper considers the problem of minimizing the time average of a controlled stochastic process subject to multiple time average constraints on other related processes. The probability distribution of the random events in the system is…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
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…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
We consider three shortest path problems in directed graphs with random arc lengths. For the first and the second problems, a risk measure is involved. While the first problem consists in finding a path minimizing this risk measure, the…
This paper will analyze several quadratic-time solvable problems, and will classify them into two classes: problems that are solvable in truly subquadratic time (that is, in time $O(n^{2-\epsilon})$ for some $\epsilon>0$) and problems that…
The paper represents an algorithm for planning safe and optimal routes for transport facilities with unrestricted movement direction that travel within areas with obstacles. Paper explains the algorithm using a ship as an example of such a…
The domination problem and its variants represent a classical domain within algorithmic graph theory. Among these variants, the paired-domination problem holds particular prominence due to its real-world implications in security and…
In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the…
The starting point of our work is a decade-old open question concerning the subexponential parameterized complexity of \textsc{2-Layer Crossing Minimization}. In this problem, the input is an $n$-vertex graph $G$ whose vertices are…
We consider the problem of assigning appearing times to the edges of a digraph in order to maximize the (average) temporal reachability between pairs of nodes. Motivated by the application to public transit networks, where edges cannot be…
It is $\mathsf{NP}$-hard to determine the minimum number of branching vertices needed in a single-source distance-preserving subgraph of an undirected graph. We show that this problem can be solved in polynomial time if the input graph is…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…
We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…
An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transversal problem which asks for an output-polynomial algorithm for listing…
Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
We consider a problem wherein jobs arrive at random times and assume random values. Upon each job arrival, the decision-maker must decide immediately whether or not to accept the job and gain the value on offer as a reward, with the…