3,702 research outputs found
Computing Temporal Reachability Under Waiting-Time Constraints in Linear Time
This paper proposes a simple algorithm for computing single-source reachability in a temporal graph under waiting-time constraints, that is when waiting at each node is bounded by some time constraints. Given a space-time representation of a temporal graph, and a source node, the algorithm computes in linear-time which nodes and temporal edges are reachable through a constrained temporal walk from the source
Minimum-Cost Temporal Walks under Waiting-Time Constraints in Linear Time
In a temporal graph, each edge is available at specific points in time. Such
an availability point is often represented by a ''temporal edge'' that can be
traversed from its tail only at a specific departure time, for arriving in its
head after a specific travel time. In such a graph, the connectivity from one
node to another is naturally captured by the existence of a temporal path where
temporal edges can be traversed one after the other. When imposing constraints
on how much time it is possible to wait at a node in-between two temporal
edges, it then becomes interesting to consider temporal walks where it is
allowed to visit several times the same node, possibly at different times. We
study the complexity of computing minimum-cost temporal walks from a single
source under waiting-time constraints in a temporal graph, and ask under which
conditions this problem can be solved in linear time. Our main result is a
linear time algorithm when temporal edges are provided in input by
non-decreasing departure time and also by non-decreasing arrival time. We use
an algebraic framework for manipulating abstract costs, enabling the
optimization of a large variety of criteria or even combinations of these. It
allows to improve previous results for several criteria such as number of edges
or overall waiting time. This result is somehow optimal: a logarithmic factor
in the time complexity appears to be necessary if the input contains only one
ordering of the temporal edges (either by arrival times or departure times)
Finding Temporal Paths Under Waiting Time Constraints
Computing 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 ?, referred to as ?-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 feedback vertex number or the pathwidth of the underlying graph. The main question thus is 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
As Time Goes By: Adding a Temporal Dimension Towards Resolving Delegations in Liquid Democracy
In recent years, the study of various models and questions related to Liquid
Democracy has been of growing interest among the community of Computational
Social Choice. A concern that has been raised, is that current academic
literature focuses solely on static inputs, concealing a key characteristic of
Liquid Democracy: the right for a voter to change her mind as time goes by,
regarding her options of whether to vote herself or delegate her vote to other
participants, till the final voting deadline. In real life, a period of
extended deliberation preceding the election-day motivates voters to adapt
their behaviour over time, either based on observations of the remaining
electorate or on information acquired for the topic at hand. By adding a
temporal dimension to Liquid Democracy, such adaptations can increase the
number of possible delegation paths and reduce the loss of votes due to
delegation cycles or delegating paths towards abstaining agents, ultimately
enhancing participation. Our work takes a first step to integrate a time
horizon into decision-making problems in Liquid Democracy systems. Our
approach, via a computational complexity analysis, exploits concepts and tools
from temporal graph theory which turn out to be convenient for our framework
Betweenness centrality for temporal multiplexes
Betweenness centrality quantifies the importance of a vertex for the
information flow in a network. We propose a flexible definition of betweenness
for temporal multiplexes, where geodesics are determined accounting for the
topological and temporal structure and the duration of paths. We propose an
algorithm to compute the new metric via a mapping to a static graph. We show
the importance of considering the temporal multiplex structure and an
appropriate distance metric comparing the results with those obtained with
static or single-layer metrics on a dataset of k European flights
Complexity of the Temporal Shortest Path Interdiction Problem
In the shortest path interdiction problem, an interdictor aims to remove arcs of total cost at most a given budget from a directed graph with given arc costs and traversal times such that the length of a shortest s-t-path is maximized. For static graphs, this problem is known to be strongly NP-hard, and it has received considerable attention in the literature.
While the shortest path problem is one of the most fundamental and well-studied problems also for temporal graphs, the shortest path interdiction problem has not yet been formally studied on temporal graphs, where common definitions of a "shortest path" include: latest start path (path with maximum start time), earliest arrival path (path with minimum arrival time), shortest duration path (path with minimum traveling time including waiting times at nodes), and shortest traversal path (path with minimum traveling time not including waiting times at nodes).
In this paper, we analyze the complexity of the shortest path interdiction problem on temporal graphs with respect to all four definitions of a shortest path mentioned above. Even though the shortest path interdiction problem on static graphs is known to be strongly NP-hard, we show that the latest start and the earliest arrival path interdiction problems on temporal graphs are polynomial-time solvable. For the shortest duration and shortest traversal path interdiction problems, however, we show strong NP-hardness, but we obtain polynomial-time algorithms for these problems on extension-parallel temporal graphs
The impact of temporal sampling resolution on parameter inference for biological transport models
Imaging data has become widely available to study biological systems at
various scales, for example the motile behaviour of bacteria or the transport
of mRNA, and it has the potential to transform our understanding of key
transport mechanisms. Often these imaging studies require us to compare
biological species or mutants, and to do this we need to quantitatively
characterise their behaviour. Mathematical models offer a quantitative
description of a system that enables us to perform this comparison, but to
relate these mechanistic mathematical models to imaging data, we need to
estimate the parameters of the models. In this work, we study the impact of
collecting data at different temporal resolutions on parameter inference for
biological transport models by performing exact inference for simple velocity
jump process models in a Bayesian framework. This issue is prominent in a host
of studies because the majority of imaging technologies place constraints on
the frequency with which images can be collected, and the discrete nature of
observations can introduce errors into parameter estimates. In this work, we
avoid such errors by formulating the velocity jump process model within a
hidden states framework. This allows us to obtain estimates of the
reorientation rate and noise amplitude for noisy observations of a simple
velocity jump process. We demonstrate the sensitivity of these estimates to
temporal variations in the sampling resolution and extent of measurement noise.
We use our methodology to provide experimental guidelines for researchers
aiming to characterise motile behaviour that can be described by a velocity
jump process. In particular, we consider how experimental constraints resulting
in a trade-off between temporal sampling resolution and observation noise may
affect parameter estimates.Comment: Published in PLOS Computational Biolog
The Parallelism Motifs of Genomic Data Analysis
Genomic data sets are growing dramatically as the cost of sequencing
continues to decline and small sequencing devices become available. Enormous
community databases store and share this data with the research community, but
some of these genomic data analysis problems require large scale computational
platforms to meet both the memory and computational requirements. These
applications differ from scientific simulations that dominate the workload on
high end parallel systems today and place different requirements on programming
support, software libraries, and parallel architectural design. For example,
they involve irregular communication patterns such as asynchronous updates to
shared data structures. We consider several problems in high performance
genomics analysis, including alignment, profiling, clustering, and assembly for
both single genomes and metagenomes. We identify some of the common
computational patterns or motifs that help inform parallelization strategies
and compare our motifs to some of the established lists, arguing that at least
two key patterns, sorting and hashing, are missing
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