Earliest arrival flows on series-parallel graphs

Earliest arrival flows on series-parallel graphs

We present an exact algorithm for computing an earliest arrival flow in a discrete time setting on series-parallel graphs. In contrast to previous results for the earliest arrival flow problem this algorithm runs in polynomial time.

A Survey on Earliest Arrival Flows and a Study of the Series-Parallel Case

Acknowledgement I am most grateful to my Lord and God Jesus Christ who is truly worthy of all praise. I especially praise and thank Him for all His help concerning this work. I am also very grateful to Jun. Prof. Dr. Stefan Ruzika for his help and guidance and especially for his patience. I also thank Heike Sperber for sharing her knowledge of series-parallel graphs with me.

Evacuation by Earliest Arrival Flows

Earliest Arrival Flows with Multiple Sources

Earliest arrival flows capture the essence of evacuation planning. Given a network with capacities and transit times on the arcs, a subset of source nodes with supplies and a sink node, the task is to send the given supplies from the sources to the sink “as quickly as possible”. The latter requirement is made more precise by the earliest arrival property which requires that the total amount of ...

Computing earliest arrival flows with multiple sources

Earliest arrival flows are motivated by applications related to evacuation. In typical evacuation situations, the most important task is to get people out of an endangered building or area as fast as possible. Since it is usually not known how long a building can withstand a fire before it collapses or how long a dam can resist a flood before it breaks, it is advisable to organize an evacuation...