--- title: Breadth-First Search TARGET DECK: Obsidian::STEM FILE TAGS: algorithm data_structure::graph tags: - bfs - graph --- ## Overview Bread-first search operates on a graph $G = \langle V, E \rangle$ and a **source** vertex $s$. It works by distinguishing between discovered and undiscovered nodes, incrementally marking nodes adjacent to discovered nodes from undiscovered to discovered. ![[bfs.gif]] %%ANKI Basic What is BFS an acronym for? Back: **B**readth-**f**irst **s**earch. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Cloze Breadth-first search is characterized by a graph and a {source vertex}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Cloze The {1:source} of breadth-first {2:search} is the {2:root} of the breadth-first {1:tree}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic Which of undirected and directed graphs is BFS applicable to? Back: Both. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic With respect to breadth-first trees, what does the predecessor of a node $N$ refer to? Back: The node from which $N$ was discovered. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic With respect to breadth-first trees, what does the parent of a node $N$ refer to? Back: The node from which $N$ was discovered. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic With respect to breadth-first trees, the predecessor of a node is also known as what? Back: The parent of the node. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic With respect to breadth-first trees, the parent of a node is also known as what? Back: The predecessor of the node. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic What ADT is typically used to manage the set of most recently discovered BFS vertices? Back: A queue. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic Which vertices are not discovered during a graph BFS? Back: Those not reachable from the source vertex. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic What basic graph algorithm is the following a demonstration of? ![[bfs.gif]] Back: Breadth-first search. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic In BFS, what happens to the nodes found within the internal queue? Back: Undiscovered nodes adjacent to those in the queue are enqueued. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic Which of BFS or DFS is used to find shortest paths? Back: BFS. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic When can BFS *not* be used to find shortest paths? Back: When the graph in question has differently weighted edges. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic Which weighted graphs can BFS be used on to find shortest paths? Back: Graphs with equally weighted edges. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic Which standard graph representation has worst-case BFS running time of $O(\lvert V \rvert + \lvert E \rvert)$? Back: The adjacency-matrix representation. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic Given graph $\langle V, E \rangle$ with adjacency-list representation, what is the worst-case run time of BFS? Back: $O(\lvert V \rvert + \lvert E \rvert)$ Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic Given graph $\langle V, E \rangle$ with adjacency-matrix representation, what is the worst-case run time of BFS? Back: $O(\lvert V \rvert^2)$ Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic *Why* is BFS of an adjacency-list representation $O(\lvert V \rvert + \lvert E \rvert)$? Back: For each vertex being analyzed, we only examine its immediately adjacent vertices. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% %%ANKI Basic *Why* is BFS of an adjacency-matrix representation $O(\lvert V \rvert^2)$? Back: For each vertex being analyzed, we must examine $\lvert V \rvert$ entries for adjacent vertices. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). END%% ## Bibliography * Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).