3,601 research outputs found
Temporal vertex cover with a sliding time window.
Modern, inherently dynamic systems are usually characterized by a network structure which is subject to discrete changes over time. Given a static underlying graph, a temporal graph can be represented via an assignment of a set of integer time-labels to every edge, indicating the discrete time steps when this edge is active. While most of the recent theoretical research on temporal graphs focused on temporal paths and other “path-related” temporal notions, only few attempts have been made to investigate “non-path” temporal problems. In this paper we introduce and study two natural temporal extensions of the classical problem VERTEX COVER. We present a thorough investigation of the computational complexity and approximability of these two temporal covering problems. We provide strong hardness results, complemented by approximation and exact algorithms. Some of our algorithms are polynomial-time, while others are asymptotically almost optimal under the Exponential Time Hypothesis (ETH) and other plausible complexity assumptions
Temporal Vertex Cover with a Sliding Time Window
Modern, inherently dynamic systems are usually characterized by a network structure, i.e. an underlying graph topology, which is subject to discrete changes over time. Given a static underlying graph , a temporal graph can be represented via an assignment of a set of integer time-labels to every edge of , indicating the discrete time steps when this edge is active. While most of the recent theoretical research on temporal graphs has focused on the notion of a temporal path and other "path-related" temporal notions, only few attempts have been made to investigate "non-path" temporal graph problems. In this paper, motivated by applications in sensor and in transportation networks, we introduce and study two natural temporal extensions of the classical problem Vertex Cover. In both cases we wish to minimize the total number of "vertex appearances" that are needed to "cover" the whole temporal graph. In our first problem, Temporal Vertex Cover, the aim is to cover every edge at least once during the lifetime of the temporal graph, where an edge can be covered by one of its endpoints, only at a time step when it is active. In our second, more pragmatic variation Sliding Window Temporal Vertex Cover, we are also given a natural number , and our aim is to cover every edge at least once at every consecutive time steps. We present a thorough investigation of the computational complexity and approximability of these two temporal covering problems. In particular, we provide strong hardness results, complemented by various approximation and exact algorithms. Some of our algorithms are polynomial-time, while others are asymptotically almost optimal under the Exponential Time Hypothesis (ETH) and other plausible complexity assumptions
Coverage centralities for temporal networks
Structure of real networked systems, such as social relationship, can be
modeled as temporal networks in which each edge appears only at the prescribed
time. Understanding the structure of temporal networks requires quantifying the
importance of a temporal vertex, which is a pair of vertex index and time. In
this paper, we define two centrality measures of a temporal vertex based on the
fastest temporal paths which use the temporal vertex. The definition is free
from parameters and robust against the change in time scale on which we focus.
In addition, we can efficiently compute these centrality values for all
temporal vertices. Using the two centrality measures, we reveal that
distributions of these centrality values of real-world temporal networks are
heterogeneous. For various datasets, we also demonstrate that a majority of the
highly central temporal vertices are located within a narrow time window around
a particular time. In other words, there is a bottleneck time at which most
information sent in the temporal network passes through a small number of
temporal vertices, which suggests an important role of these temporal vertices
in spreading phenomena.Comment: 13 pages, 10 figure
Sliding window temporal graph coloring
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 graphs, which often stand in contrast to practice where data is inherently dynamic. A temporal graph has an edge set that changes over time. We present a natural temporal extension of the classical graph coloring problem. Given a temporal graph and integers k and Δ, we ask for a coloring sequence with at most k colors for each vertex such that in every time window of Δ consecutive time steps, in which an edge is present, this edge is properly colored at least once. We thoroughly investigate the computational complexity of this temporal coloring problem. More specifically, we prove strong computational hardness results, complemented by efficient exact and approximation algorithms
Benchmarks for Parity Games (extended version)
We propose a benchmark suite for parity games that includes all benchmarks
that have been used in the literature, and make it available online. We give an
overview of the parity games, including a description of how they have been
generated. We also describe structural properties of parity games, and using
these properties we show that our benchmarks are representative. With this work
we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from
https://github.com/jkeiren/paritygame-generator. This is an extended version
of the paper that has been accepted for FSEN 201
Action Recognition by Hierarchical Mid-level Action Elements
Realistic videos of human actions exhibit rich spatiotemporal structures at
multiple levels of granularity: an action can always be decomposed into
multiple finer-grained elements in both space and time. To capture this
intuition, we propose to represent videos by a hierarchy of mid-level action
elements (MAEs), where each MAE corresponds to an action-related spatiotemporal
segment in the video. We introduce an unsupervised method to generate this
representation from videos. Our method is capable of distinguishing
action-related segments from background segments and representing actions at
multiple spatiotemporal resolutions. Given a set of spatiotemporal segments
generated from the training data, we introduce a discriminative clustering
algorithm that automatically discovers MAEs at multiple levels of granularity.
We develop structured models that capture a rich set of spatial, temporal and
hierarchical relations among the segments, where the action label and multiple
levels of MAE labels are jointly inferred. The proposed model achieves
state-of-the-art performance in multiple action recognition benchmarks.
Moreover, we demonstrate the effectiveness of our model in real-world
applications such as action recognition in large-scale untrimmed videos and
action parsing
- …