Title:
Accurately and Efficiently Estimating Dynamic Point-to-Point Shortest Path
Accurately and Efficiently Estimating Dynamic Point-to-Point Shortest Path
Author(s)
Tripathy, Alok
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Abstract
Point-to-point shortest path (PPSP), or s-t connectivity, is a
variant of the shortest path problem found in graph theory. In
this problem, we are given a graph and pairs of vertices over
time, and the output is the shortest path between each pair
of vertices. In this paper, we present two algorithms. Our first
algorithm approximately solves the PPSP problem on any
arbitrary graph. For each pair of vertices queried, it accurately
and efficiently estimates the shortest path between the two
vertices. Our second algorithm extends the first to work on
dynamic graphs. That is, our second algorithm can efficiently
account for changes in the graph, such as friend requests
on the Facebook network or road closures on road networks.
At a high level, both algorithms partition the graph into
highly connected communities. To respond to a query q(u, v),
they each find the fewest number of partitions between u
and v, and the shortest path through each partition. We
show that our static graph algorithm can approximate the
distance between two vertices with about 20% − 35% percent
error and anywhere from 80X − 70000X faster than a BFS
in practice with the right choice of partitions. Additionally,
we show that our dynamic graph algorithm can account for
updates to the graph anywhere from 20X − 20000X faster
than rerunning the static graph algorithm for each change to
the graph.
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Date Issued
2019-05
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Resource Type
Text
Resource Subtype
Undergraduate Thesis