Temporal matching

Baste, Julien; Bui-Xuan, Binh-Minh; Roux, Antoine

doi:10.1016/j.tcs.2019.03.026

Cited by 17 publications

(20 citation statements)

References 19 publications

(22 reference statements)

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“…In fact, many temporal (matching) problems turn out to be hard, even w.r.t. approximation and fixed-parameter-tractability [1,6,10,20,21].…”

Section: Related Workmentioning

confidence: 99%

Approximating Multistage Matching Problems

Chimani¹,

Troost²,

Wiedera³

2020

Preprint

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In multistage perfect matching problems we are given a sequence of graphs on the same vertex set and asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as possible. More precisely, we aim to maximize the intersections, or minimize the unions between consecutive matchings. We show that these problems are NP-hard even in very restricted scenarios.We propose new approximation algorithms and present methods to transfer results between different problem variants without loosing approximation guarantees.

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“…In fact, many temporal (matching) problems turn out to be hard, even w.r.t. approximation and fixed-parameter-tractability [1,6,10,20,21].…”

Section: Related Workmentioning

confidence: 99%

Approximating Multistage Matching Problems

Chimani¹,

Troost²,

Wiedera³

2020

Preprint

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“…Driven by this NP-hardness, Mertzios et al [11] showed an FPT-algorithm for Temporal Matching, when parameterized by ∆ and the maximum matching size of the underlying graph G ↓ (G) := (V, τ i=1 E i ) of the input temporal graph G = (V, (E t ) τ t=1 ). On a historical note, one has to mention that Baste et al [3] introduced temporal matchings in a slightly different way. The main difference to the model of Mertzios et al [11] which we also adopt here is that the model of Baste et al [3] requires edges to exist in at least ∆ consecutive time steps in order for them to be eligible for a matching.…”

Section: Temporal Matching Inputmentioning

confidence: 99%

“…On a historical note, one has to mention that Baste et al [3] introduced temporal matchings in a slightly different way. The main difference to the model of Mertzios et al [11] which we also adopt here is that the model of Baste et al [3] requires edges to exist in at least ∆ consecutive time steps in order for them to be eligible for a matching. However, with little preprocessing an instance of the model of Baste et al [3] can be reduced to our model and the algorithmic ideas presented by Baste et al [3] apply as well.…”

Section: Temporal Matching Inputmentioning

confidence: 99%

“…Matchings are one of the most fundamental and best studied notions in graph theory, see Lovász and Plummer [10] and Schrijver [13] for an overview. Recently, Baste et al [3] and Mertzios et al [11] studied matchings in temporal graphs. A temporal graph G = (V, (E t ) τ t=1 ) consists of a set V of vertices and an ordered list of τ edge sets E 1 , E 2 , .…”

Section: Introductionmentioning

confidence: 99%

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A Faster Parameterized Algorithm for Temporal Matching

Zschoche¹

2020

Preprint

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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 ∆-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 ′ ) ∈ M we have that e and e ′ do not share an endpoint, or the time-labels t and t ′ are at least ∆ time units apart. Mertzios et al. [STACS '20] provided a 2 O(∆ν) • |G| O(1) -time algorithm to compute the maximum size of ∆-temporal matching in a temporal graph G, where |G| denotes the size of G, and ν is the ∆-vertex cover number of G. The ∆-vertex cover number is the minimum number of vertices which are needed to hit (or cover) all edges in any ∆ consecutive layers of the temporal graph. We show an improved algorithm to compute a ∆-temporal matching of maximum size with a running time of ∆ O(ν) • |G| and hence provide an exponential speedup in terms of ∆.

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“…It is then proved that the problem is NP-Hard. Baste et al [3] define another type of temporal matching called γ-matching. γ-edges are defined as edges which exist for at least γ consecutive timesteps.…”

Section: Related Workmentioning

confidence: 99%

0-1 Timed Matching in Bipartite Temporal Graphs

Mandal

Gupta

2020

Lecture Notes in Computer Science

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Temporal graphs are graphs where the topology and/or other properties of the graph change with time. They have been used to model applications with temporal information in various domains. Problems on static graphs become more challenging to solve in temporal graphs because of dynamically changing topology, and many recent works have explored graph problems on temporal graphs. In this paper, we define a type of matching called 0-1 timed matching for temporal graphs, and investigate the problem of finding a maximum 0-1 timed matching for different classes of temporal graphs. We first prove that the problem is NP-Complete for rooted temporal trees when each edge is associated with two or more time intervals. We then propose an O(n 3) time algorithm for the problem on a rooted temporal tree with n nodes when each edge is associated with exactly one time interval. The problem is then shown to be NP-Complete also for bipartite temporal graphs even when each edge is associated with a single time interval and degree of each node is bounded by a constant k ≥ 3. We next investigate approximation algorithms for the problem for temporal graphs where each edge is associated with more than one time intervals. It is first shown that there is no 1 n 1−-factor approximation algorithm for the problem for any > 0 even on a rooted temporal tree with n nodes unless NP = ZPP. We then present a 1 N * +1-factor approximation algorithm for the problem for general temporal graphs where N * is the average number of edges overlapping in time with each edge in the temporal graph. The same algorithm is also a constant-factor approximation algorithm for degree bounded temporal graphs.

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Temporal matching

Cited by 17 publications

References 19 publications

Approximating Multistage Matching Problems

Approximating Multistage Matching Problems

A Faster Parameterized Algorithm for Temporal Matching

0-1 Timed Matching in Bipartite Temporal Graphs

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