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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2019.131
URN: urn:nbn:de:0030-drops-107071
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10707/
Akrida, Eleni C. ;
Mertzios, George B. ;
Nikoletseas, Sotiris ;
Raptopoulos, Christoforos ;
Spirakis, Paul G. ;
Zamaraev, Viktor
How Fast Can We Reach a Target Vertex in Stochastic Temporal Graphs?
Abstract
Temporal graphs are used to abstractly model real-life networks that are inherently dynamic in nature, in the sense that the network structure undergoes discrete changes over time. Given a static underlying graph G=(V,E), a temporal graph on G is a sequence of snapshots {G_t=(V,E_t) subseteq G: t in N}, one for each time step t >= 1. In this paper we study stochastic temporal graphs, i.e. stochastic processes G={G_t subseteq G: t in N} whose random variables are the snapshots of a temporal graph on G. A natural feature of stochastic temporal graphs which can be observed in various real-life scenarios is a memory effect in the appearance probabilities of particular edges; that is, the probability an edge e in E appears at time step t depends on its appearance (or absence) at the previous k steps. In this paper we study the hierarchy of models memory-k, k >= 0, which address this memory effect in an edge-centric network evolution: every edge of G has its own probability distribution for its appearance over time, independently of all other edges. Clearly, for every k >= 1, memory-(k-1) is a special case of memory-k. However, in this paper we make a clear distinction between the values k=0 ("no memory") and k >= 1 ("some memory"), as in some cases these models exhibit a fundamentally different computational behavior for these values of k, as our results indicate. For every k >= 0 we investigate the computational complexity of two naturally related, but fundamentally different, temporal path (or journey) problems: {Minimum Arrival} and {Best Policy}. In the first problem we are looking for the expected arrival time of a foremost journey between two designated vertices {s},{y}. In the second one we are looking for the expected arrival time of the best policy for actually choosing a particular {s}-{y} journey. We present a detailed investigation of the computational landscape of both problems for the different values of memory k. Among other results we prove that, surprisingly, {Minimum Arrival} is strictly harder than {Best Policy}; in fact, for k=0, {Minimum Arrival} is #P-hard while {Best Policy} is solvable in O(n^2) time.
BibTeX - Entry
@InProceedings{akrida_et_al:LIPIcs:2019:10707,
author = {Eleni C. Akrida and George B. Mertzios and Sotiris Nikoletseas and Christoforos Raptopoulos and Paul G. Spirakis and Viktor Zamaraev},
title = {{How Fast Can We Reach a Target Vertex in Stochastic Temporal Graphs\l{}}},
booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
pages = {131:1--131:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-109-2},
ISSN = {1868-8969},
year = {2019},
volume = {132},
editor = {Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10707},
URN = {urn:nbn:de:0030-drops-107071},
doi = {10.4230/LIPIcs.ICALP.2019.131},
annote = {Keywords: Temporal network, stochastic temporal graph, temporal path, #P-hard problem, polynomial-time approximation scheme}
}
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Keywords: |
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Temporal network, stochastic temporal graph, temporal path, #P-hard problem, polynomial-time approximation scheme |
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Collection: |
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46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) |
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Issue Date: |
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2019 |
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Date of publication: |
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04.07.2019 |
