Looking for speedups for A* search - a-star

Question

I've got the following working A* code in C#:
static bool AStar(
IGraphNode start,
Func<IGraphNode, bool> check,
out List<IGraphNode> path)
{
// Closed list. Hashset because O(1).
var closed =
new HashSet<IGraphNode>();
// Binary heap which accepts multiple equivalent items.
var frontier =
new MultiHeap<IGraphNode>(
(a, b) =>
{ return Math.Sign(a.TotalDistance - b.TotalDistance); }
);
// Some way to know how many multiple equivalent items there are.
var references =
new Dictionary<IGraphNode, int>();
// Some way to know which parent a graph node has.
var parents =
new Dictionary<IGraphNode, IGraphNode>();
// One new graph node in the frontier,
frontier.Insert(start);
// Count the reference.
references[start] = 1;
IGraphNode current = start;
do
{
do
{
frontier.Get(out current);
// If it's in the closed list or
// there's other instances of it in the frontier,
// and there's still nodes left in the frontier,
// then that's not the best node.
} while (
(closed.Contains(current) ||
(--references[current]) > 0) &&
frontier.Count > 0
);
// If we have run out of options,
if (closed.Contains(current) && frontier.Count == 0)
{
// then there's no path.
path = null;
return false;
}
closed.Add(current);
foreach (var edge in current.Edges)
{
// If there's a chance of a better path
// to this node,
if (!closed.Contains(edge.End))
{
int count;
// If the frontier doesn't contain this node,
if (!references.TryGetValue(edge.End, out count) ||
count == 0)
{
// Initialize it and insert it.
edge.End.PathDistance =
current.PathDistance + edge.Distance;
edge.End.EstimatedDistance = CalcDistance(edge.End);
parents[edge.End] = current;
frontier.Insert(edge.End);
references[edge.End] = 1;
}
else
{
// If this path is better than the existing path,
if (current.PathDistance + edge.Distance <
edge.End.PathDistance)
{
// Use this path.
edge.End.PathDistance = current.PathDistance +
edge.Distance;
parents[edge.End] = current;
frontier.Insert(edge.End);
// Keeping track of multiples equivalent items.
++references[edge.End];
}
}
}
}
} while (!check(current) && frontier.Count > 0);
if (check(current))
{
path = new List<IGraphNode>();
path.Add(current);
while (current.PathDistance != 0)
{
current = parents[current];
path.Add(current);
}
path.Reverse();
return true;
}
// Yep, no path.
path = null;
return false;
}
How do I make it faster? No code samples, please; that's a challenge I've set myself.
Edit: To clarify, I'm looking for any advice, suggestions, links, etc. that apply to A* in general. The code is just an example. I asked for no code samples because they make it too easy to implement the technique(s) being described.
Thanks.

Answer 1

Have you looked at this page or this page yet? They have plenty of helpful optimization tips as well as some great information on A* in general.

Answer 2

Change to using a Random Meldable Queue for the heap structure. Since you wanted a programming challenge, I won't show you how I changed the recursive Meld method to not be recursive. That's the trick to getting speed out of that structure. More info in Gambin's paper "Randomized Meldable Priority Queues" (search on the web for that).