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Browsing the wikipedia I got to this page where it is said: Finding k shortest paths is possible by extending Dijkstra algorithm or Bellman-Ford algorithm and extend them to find more than one pa …

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 - …

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 …

Actually, grid graphs are a very specific class of input problems, and a good number of algorithms are known that can solve problems which remain hard in other instances, i.e., non-grid graphs. Even …

That's not entirely correct Tobi. Breadth-First search requires to store in memory only those nodes awaiting for expansion. Thus, it only requires to store in memory $b^d$ nodes in the worst case, i.e …

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 …

The answer to your question is, in both cases, No. The reason is as follows: Both depth-first search and breadth-first search are uninformed search algorithms. A distinctive feature of these algorit …

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 …

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 …

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 …

Let me please start by succintly summarizing the behaviour of RBFS. For a thorough explanation of the algorithm refer to the original journal paper: Richard Korf. Linear-space best-first search. Artif …

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 …

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 …

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 …

¡Nice question really! The book is right and it just suffices for the path cost to be a nondecreasing function of the depth of the node ---though an additional note should be posted, see below. This …