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In a nutshell: IDA* traverses all paths of lengths iteratively larger and it stops only when expanding (as opposed to generating) the goal node with a cost such that all paths of an inferior cost have …

Absolutely yes! your arguments are correct. And, as matter of fact, it is very easy to come up with a graph where Bidirectional Dijkstra would expand more nodes than Unidirectional Dijkstra, following …

The only additional constraint which is required for $h_3$ and $h_4$ to be admissible is that both $h_1(n)$ and $h_2(n)$ return non-negative values for any state $n$, but this is always accomplished - …

Two components $G_1(V_1, E_1)$ and $G_2(V_2, E_2)$ are connected if and only if there is a path between any vertex $v_1\in V_1$ and any other vertex $v_2\in V_2$. Here I'm assuming that both component …

Hi there CoderInNetwork, That ain't an easy question and any advances regarding a good heuristic function would be very welcome. Indeed, I will refer in my answer to Andreas Junghanns' PhD written in …

Since you already implemented IDA$^*$ you certainly understand why it expands more nodes than A$^*$, i.e., it starts from the start state with a new depth-first traversal in each iteration. Note first …

Shaull's answer is absolutely correct, and by referring Zermelo's theorem it is pointing in the right direction. However, beyond the observations done on the rationality of your opponent, the point …

That list would be endless ... I will just try to provide a number of representative examples according to different criteria: Best-first search (BFS): they are complete, i.e., they are guaranteed to …

Nicholas already provided a perfect answer. However, let me address your original attempt to use depth-first search. First, either Dijkstra (which works fine with unweighted nodes as noted by Nichola …

[previously appearing in cstheory, it was closed there and introduced here instead] Given an edge-weighted graph $G=(V,E)$ the problem of finding the shortest path is known to be in P ---and indeed a …

Truth to be told, I am not completely sure about my answer, so take it with a grain of salt: Uniform Cost Search is just a variant of Best-First Search. Among other variants, take Breadth-First Sear …

From a general point of view: there are tons, but I do sincerely recommend you the latest volume on Heuristic Search: Heuristic Search: Theory and Applications by Stefan Edelkamp and Stefan Schroedl. …

This problem is known as the Target Value Search Problem (TVS) and it can be succintly described as follows: Given a graph $G(V,E)$, two nodes $s$ and $t$ ($s, t\in V)$ and a target value $T$ find a …

This is a nice question! Indeed, A* is known to be asymptotically optimal in the number of expansions. This is usually understood by saying that any algorithm solving the same problem should expand th …

From your question I assume you understand how symmetries are computed. As an exercise, make sure to understand the example given in Figure 4 which refers to the easiest of all symmetries, the Mirror …