TY - GEN

T1 - Temporal Unit Interval Independent Sets

AU - Hermelin, Danny

AU - Itzhaki, Yuval

AU - Molter, Hendrik

AU - Niedermeier, Rolf

N1 - Funding Information:
D. Hermelin and H. Molter are supported by the ISF, grant No. 1070/20.
Publisher Copyright:
© Danny Hermelin, Yuval Itzhaki, Hendrik Molter, and Rolf Niedermeier; licensed under Creative Commons License CC-BY 4.0

PY - 2022/4/1

Y1 - 2022/4/1

N2 - Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. We introduce and investigate the Temporal ∆ Independent Set problem, a temporal variant of the well known Independent Set problem. This problem is e.g. motivated in the context of finding conflict-free schedules for maximum subsets of tasks, that have certain (changing) constraints on each day they need to be performed. We are specifically interested in the case where each task needs to be performed in a certain time-interval on each day and two tasks are in conflict on a day if their time-intervals overlap on that day. This leads us to considering Temporal ∆ Independent Set on the restricted class of temporal unit interval graphs, i.e., temporal graphs where each layer is unit interval. We present several hardness results for this problem, as well as two algorithms: The first is a constant-factor approximation algorithm for instances where τ, the total number of time steps (layers) of the temporal graph, and ∆, a parameter that allows us to model some tolerance in the conflicts, are constants. For the second result we use the notion of order preservation for temporal unit interval graphs that, informally, requires the intervals of every layer to obey a common ordering. We provide an FPT algorithm parameterized by the size of minimum vertex deletion set to order preservation.

AB - Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. We introduce and investigate the Temporal ∆ Independent Set problem, a temporal variant of the well known Independent Set problem. This problem is e.g. motivated in the context of finding conflict-free schedules for maximum subsets of tasks, that have certain (changing) constraints on each day they need to be performed. We are specifically interested in the case where each task needs to be performed in a certain time-interval on each day and two tasks are in conflict on a day if their time-intervals overlap on that day. This leads us to considering Temporal ∆ Independent Set on the restricted class of temporal unit interval graphs, i.e., temporal graphs where each layer is unit interval. We present several hardness results for this problem, as well as two algorithms: The first is a constant-factor approximation algorithm for instances where τ, the total number of time steps (layers) of the temporal graph, and ∆, a parameter that allows us to model some tolerance in the conflicts, are constants. For the second result we use the notion of order preservation for temporal unit interval graphs that, informally, requires the intervals of every layer to obey a common ordering. We provide an FPT algorithm parameterized by the size of minimum vertex deletion set to order preservation.

KW - Algorithms

KW - Complexity

KW - Interval Graphs

KW - Order Preservation

KW - Temporal Graphs

KW - Vertex Orderings

UR - http://www.scopus.com/inward/record.url?scp=85130793522&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.SAND.2022.19

DO - 10.4230/LIPIcs.SAND.2022.19

M3 - Conference contribution

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022

A2 - Aspnes, James

A2 - Michail, Othon

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022

Y2 - 28 March 2022 through 30 March 2022

ER -