scholarly journals Finding Temporal Paths Under Waiting Time Constraints

Algorithmica ◽  
2021 ◽  
Author(s):  
Arnaud Casteigts ◽  
Anne-Sophie Himmel ◽  
Hendrik Molter ◽  
Philipp Zschoche
Keyword(s):  
Communication Networks ◽  
Waiting Time ◽  
Fpt Algorithms ◽  
Vertex Number ◽  
Underlying Graph ◽  
Time Restrictions ◽  
Time Stamps ◽  
Vertex Set ◽  
Restrictive Settings ◽  
Natural Settings

AbstractComputing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes over time, gained more and more attention. A path is time-respecting, or temporal, if it uses edges with non-decreasing time stamps. We investigate a basic constraint for temporal paths, where the time spent at each vertex must not exceed a given duration $$\varDelta $$ Δ , referred to as $$\varDelta $$ Δ -restless temporal paths. This constraint arises naturally in the modeling of real-world processes like packet routing in communication networks and infection transmission routes of diseases where recovery confers lasting resistance. While finding temporal paths without waiting time restrictions is known to be doable in polynomial time, we show that the “restless variant” of this problem becomes computationally hard even in very restrictive settings. For example, it is W[1]-hard when parameterized by the distance to disjoint path of the underlying graph, which implies W[1]-hardness for many other parameters like feedback vertex number and pathwidth. A natural question is thus whether the problem becomes tractable in some natural settings. We explore several natural parameterizations, presenting FPT algorithms for three kinds of parameters: (1) output-related parameters (here, the maximum length of the path), (2) classical parameters applied to the underlying graph (e.g., feedback edge number), and (3) a new parameter called timed feedback vertex number, which captures finer-grained temporal features of the input temporal graph, and which may be of interest beyond this work.

scholarly journals On Structural Parameterizations of the Edge Disjoint Paths Problem

Algorithmica ◽  
2021 ◽  
Author(s):  
Robert Ganian ◽  
Sebastian Ordyniak ◽  
M. S. Ramanujan
Keyword(s):  
Polynomial Time ◽  
Disjoint Paths ◽  
Structural Parameter ◽  
Input Graph ◽  
Feedback Vertex Set ◽  
Fpt Algorithms ◽  
Edge Disjoint ◽  
Fpt Algorithm ◽  
Vertex Set ◽  
Terminal Pair

AbstractIn this paper we revisit the classical edge disjoint paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our focus lies on structural parameterizations for the problem that allow for efficient (polynomial-time or FPT) algorithms. As our first result, we answer an open question stated in Fleszar et al. (Proceedings of the ESA, 2016), by showing that the problem can be solved in polynomial time if the input graph has a feedback vertex set of size one. We also show that EDP parameterized by the treewidth and the maximum degree of the input graph is fixed-parameter tractable. Having developed two novel algorithms for EDP using structural restrictions on the input graph, we then turn our attention towards the augmented graph, i.e., the graph obtained from the input graph after adding one edge between every terminal pair. In constrast to the input graph, where EDP is known to remain -hard even for treewidth two, a result by Zhou et al. (Algorithmica 26(1):3--30, 2000) shows that EDP can be solved in non-uniform polynomial time if the augmented graph has constant treewidth; we note that the possible improvement of this result to an FPT-algorithm has remained open since then. We show that this is highly unlikely by establishing the [1]-hardness of the problem parameterized by the treewidth (and even feedback vertex set) of the augmented graph. Finally, we develop an FPT-algorithm for EDP by exploiting a novel structural parameter of the augmented graph.

scholarly journals Fast Change Point Detection on Dynamic Social Networks

2017 ◽  
Author(s):  
Yu Wang ◽  
Aniket Chakrabarti ◽  
David Sivakoff ◽  
Srinivasan Parthasarathy
Keyword(s):  
Communication Networks ◽  
Real World ◽  
Change Point ◽  
Dynamic Networks ◽  
Change Point Detection ◽  
Logical Time ◽  
Dynamic Social Networks ◽  
Fast Change ◽  
Time Stamps ◽  
Point Detection

A number of real world problems in many domains (e.g. sociology, biology, political science and communication networks) can be modeled as dynamic networks with nodes representing entities of interest and edges representing interactions among the entities at different points in time. A common representation for such models is the snapshot model - where a network is defined at logical time-stamps. An important problem under this model is change point detection. In this work we devise an effective and efficient three-step-approach for detecting change points in dynamic networks under the snapshot model. Our algorithm achieves up to 9X speedup over the state-of-the-art while improving quality on both synthetic and real world networks.

scholarly journals FPT Algorithms for Connected Feedback Vertex Set

2010 ◽  
pp. 269-280 ◽  
Author(s):  
Neeldhara Misra ◽  
Geevarghese Philip ◽  
Venkatesh Raman ◽  
Saket Saurabh ◽  
Somnath Sikdar
Keyword(s):  
Feedback Vertex Set ◽  
Fpt Algorithms ◽  
Vertex Set

Note on Reliability Analysis of Cartesian Product of Networks for Components

2021 ◽  
pp. 2142010
Author(s):  
Litao Guo ◽  
Jun Ge
Keyword(s):  
Reliability Analysis ◽  
Critical Parameter ◽  
Cartesian Product ◽  
Schwarz Inequality ◽  
Large Network ◽  
Vertex Number ◽  
Cartesian Product Of Graphs ◽  
Vertex Set ◽  
Product Of Graphs ◽  
Text Component

Connectivity is a critical parameter which can measure the reliability of networks. Let [Formula: see text] be a vertex set of [Formula: see text]. If [Formula: see text] has at least [Formula: see text] components, then [Formula: see text] is a [Formula: see text]-component cut of [Formula: see text]. The [Formula: see text]-component connectivity [Formula: see text] of [Formula: see text] is the vertex number of a smallest [Formula: see text]-component cut. Cartesian product of graphs is a useful method to construct a large network. We will use Cauchy–Schwarz inequality to determine the component connectivity of Cartesian product of some graphs.

scholarly journals Delay Analysis of anM/G/1/KPriority Queueing System with Push-out Scheme

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Yutae Lee ◽  
Bong Dae Choi ◽  
Bara Kim ◽  
Dan Keun Sung
Keyword(s):  
Communication Networks ◽  
Waiting Time ◽  
Queueing System ◽  
Waiting Times ◽  
Loss Probability ◽  
Mean Waiting Time ◽  
The Mean ◽  
Recursive Equations ◽  
Push Out ◽  
Stieltjes Transforms

This paper considers anM/G/1/Kqueueing system with push-out scheme which is one of the loss priority controls at a multiplexer in communication networks. The loss probability for the model with push-out scheme has been analyzed, but the waiting times are not available for the model. Using a set of recursive equations, this paper derives the Laplace-Stieltjes transforms (LSTs) of the waiting time and the push-out time of low-priority messages. These results are then utilized to derive the loss probability of each traffic type and the mean waiting time of high-priority messages. Finally, some numerical examples are provided.

scholarly journals FPT algorithms for Connected Feedback Vertex Set

2011 ◽  
Vol 24 (2) ◽  
pp. 131-146 ◽  
Author(s):  
Neeldhara Misra ◽  
Geevarghese Philip ◽  
Venkatesh Raman ◽  
Saket Saurabh ◽  
Somnath Sikdar
Keyword(s):  
Feedback Vertex Set ◽  
Fpt Algorithms ◽  
Vertex Set

scholarly journals FPT Algorithms for Diverse Collections of Hitting Sets

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 254
Author(s):  
Julien Baste ◽  
Lars Jaffke ◽  
Tomáš Masařík ◽  
Geevarghese Philip ◽  
Günter Rote
Keyword(s):  
Network Flow ◽  
Hamming Distance ◽  
Side Information ◽  
Feedback Vertex Set ◽  
Fixed Parameter Tractable ◽  
Fpt Algorithms ◽  
Fixed Parameter ◽  
Vertex Set ◽  
Two Measures ◽  
Real World Problems

In this work, we study the d-Hitting Set and Feedback Vertex Set problems through the paradigm of finding diverse collections of r solutions of size at most k each, which has recently been introduced to the field of parameterized complexity. This paradigm is aimed at addressing the loss of important side information which typically occurs during the abstraction process that models real-world problems as computational problems. We use two measures for the diversity of such a collection: the sum of all pairwise Hamming distances, and the minimum pairwise Hamming distance. We show that both problems are fixed-parameter tractable in k + r for both diversity measures. A key ingredient in our algorithms is a (problem independent) network flow formulation that, given a set of ‘base’ solutions, computes a maximally diverse collection of solutions. We believe that this could be of independent interest.

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