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COMPSCI4009 Algorithmics I (H) 2025-26

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Let

G be an undirected connected graph with distinct edge weights, i.e. no two edges have the same weight, emax be the edge with maximum weight and emin

the edge with

minimum weight.

Which of the following statements is false?

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In a weighted, undirected graph if we apply Prim Jarnak's algorithm

to find the minimum weight spanning tree. If we add 1 to all the

edge weights, does the minimum weight spanning tree always

remain the same?

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What is the complexity of breath first search when using an

adjacency list representation for an undirected graph with n vertices

and m edges?

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In a weighted, directed graph if we apply Dijkstra's algorithm to find

the shortest path between two nodes. If we add 1 to all the edge

weights, does the shortest path always remain the same?

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If all edges have the same weight in an undirected graph, which

algorithm will find the shortest path between two nodes more

efficiently?

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In the table required by the BM algorithm when searching for the pattern s in the text t, what value is given for character a of the alphabet?
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What is the length of the longest border of abcabca?
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In the table required by the KMP algorithm what is

included in entry

i when searching for the pattern/string s?

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What property of the dictionary holds throughout the running of the

LZW algorithm?

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Assuming the character frequencies have already been found, what

is the complexity of building a Huffman tree if there are

m characters?
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