A Hybrid Approach to Temporal Pattern Matching

A Faster Parameterized Algorithm for Temporal Matching

A temporal graph is a sequence of graphs (called layers) over the same vertex set -- describing a graph topology which is subject to discrete changes over time. A $Δ$-temporal matching $M$ is a set of time edges $(e,t)$ (an edge $e$ paired up with a point in time $t$) such that for all distinct time edges $(e,t),(e',t') \in M$ we have that $e$ and $e'$ do not share an endpoint, or the time-labels $t$ and $t'$ are at least $Δ$ time units apart. Mertzios et al. [STACS '20] provided a $2^{O(Δν)}\cdot |{\mathcal G}|^{O(1)}$-time algorithm to compute the maximum size of a $Δ$-temporal matching in a…

Temporal Matching

A link stream is a sequence of pairs of the form $(t,\{u,v\})$, where $t\in\mathbb N$ represents a time instant and $u\neq v$. Given an integer $γ$, the $γ$-edge between vertices $u$ and $v$, starting at time $t$, is the set of temporally consecutive edges defined by $\{(t',\{u,v\}) | t' \in [t,t+γ-1]\}$. We introduce the notion of temporal matching of a link stream to be an independent $γ$-edge set belonging to the link stream. We show that the problem of computing a temporal matching of maximum size is NP-hard as soon as $γ>1$. We depict a kernelization algorithm parameterized by the solutio…

时间图中的匹配与边覆盖

Matching and Edge Cover in Temporal Graphs

本文定义时间边覆盖和时间匹配问题，证明其NP完全性，并给出基于生命周期和树宽的FPT算法及匹配下界的近似算法。

Computing Maximum Matchings in Temporal Graphs

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the discrete time steps at which $e$ is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) $(e,t)$ su…

THAAD: Efficient Matching Queries under Temporal Abstraction for Anomaly Detection

In this paper we present a novel algorithm and efficient data structure for anomaly detection based on temporal data. Time-series data are represented by a sequence of symbolic time intervals, describing increasing and decreasing trends, in a compact way using gradient temporal abstraction technique. Then we identify unusual subsequences in the resulting sequence using dynamic data structure based on the geometric observations supporting polylogarithmic update and query times. Moreover, we introduce a new parameter to control the pairwise difference between the corresponding symbols in additio…

A Chronological Edge-Driven Approach to Temporal Subgraph Isomorphism

Many real world networks are considered temporal networks, in which the chronological ordering of the edges has importance to the meaning of the data. Performing temporal subgraph matching on such graphs requires the edges in the subgraphs to match the order of the temporal graph motif we are searching for. Previous methods for solving this rely on the use of static subgraph matching to find potential matches first, before filtering them based on edge order to find the true temporal matches. We present a new algorithm for temporal subgraph isomorphism that performs the subgraph matching direct…

When Hashing Met Matching: Efficient Spatio-Temporal Search for Ridesharing

Carpooling, or sharing a ride with other passengers, holds immense potential for urban transportation. Ridesharing platforms enable such sharing of rides using real-time data. Finding ride matches in real-time at urban scale is a difficult combinatorial optimization task and mostly heuristic approaches are applied. In this work, we mathematically model the problem as that of finding near-neighbors and devise a novel efficient spatio-temporal search algorithm based on the theory of locality sensitive hashing for Maximum Inner Product Search (MIPS). The proposed algorithm can find $k$ near-optim…

A Hybrid Adjacency and Time-Based Data Structure for Analysis of Temporal Networks

Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus quickly retrieve all edges between two sets of nodes (a node-based slice) but cannot quickly retrieve all edges that occur within a given time interval (a time-based slice). We propose a hybrid data structure for storing temporal networks that stores edges in both an adjacency dictionary, enabling rapid node-based slices, and an interval tree, enabling rapid ti…