Neo4J.

1 files changed, 15 insertions, 16 deletions

diff --git a/_blog/neo4j-a-star-search.md b/_blog/neo4j-a-star-search.md
index 117931b..e52dad9 100644
--- a/_blog/neo4j-a-star-search.md
+++ b/_blog/neo4j-a-star-search.md
@@ -7,24 +7,23 @@ layout: post
 Back in 2018, we used <a href="https://neo4j.com/" class="external"
 target="_blank" rel="noopener noreferrer">Neo4J</a> graph database to track the
 movement of marine vessels. We were interested in the shortest path a ship
-could take through a network of about 13,000 route points. Algorithms based on
-graph theory, such as A* search, provide optimal solutions to such problems.
-In other words, the set of route points lends itself well to a model based on
-graphs.
+could take through a network of about 13,000 route points. Graph theoretic
+algorithms provide optimal solutions to such problems, and the set of route
+points lends itself well to graph-based modelling.
 
 A graph is a finite set of vertices, and a subset of vertex pairs (edges).
 Edges can have weights. In the case of vessel tracking, the route points form
-the vertices of a graph; the routes between them, the edges; and the distances
-between them are the weights. For different reasons, people are interested in
-minimizing (or maximizing) the weight of a path through a set of vertices. For
-instance, we may want to find the shortest path between two ports.
-
-Given such a graph, an algorithm like Dijkstra's search could compute the
-shortest path between two vertices. In fact, this was the algorithm Neo4J
-shipped with at the time. One drawback of Dijkstra's algorithm is that it
-computes all the shortest paths from the source to all other vertices before
-terminating at the destination vertex. The exhaustive nature of this search
-limited our search to about 4,000 route points.
+the vertices of a graph; the routes between them the edges; and the distances
+between them the weights. For various reasons, people are interested in
+minimizing (or maximizing) the weight of a path through a set of vertices, such
+as the shortest path between two ports to predict a vessel's arrival time.
+
+Given a graph, an algorithm like Dijkstra's search could compute the shortest
+path between two vertices. In fact, this was the algorithm Neo4J shipped with
+at the time. One drawback of Dijkstra's algorithm is that it computes all the
+shortest paths from the source to all other vertices before terminating at the
+destination vertex. The time complexity of this exhaustive search prevented our
+database from scaling beyond 4,000 route points.
 
 The following enhancement to Dijkstra's search, also known as the A* search,
 employs a heuristic to steer the search in the direction of the destination
@@ -314,5 +313,5 @@ significantly speed up the search. In our case, we achieved a 300x speedup,
 enabling us to expand our search from 4,000 to 13,000 route points. The <a
 href="https://github.com/neo4j-contrib/neo4j-graph-algorithms/releases/tag/3.4.0.0"
 class="external" target="_blank" rel="noopener noreferrer">v3.4.0</a> of the
-Neo4J graph algorithms shipped with the A* search algorithm.
+Neo4J graph algorithms shipped with our A* search algorithm.