Consider a graph G with n nodes and m edges, where n m (i.e. G is a sparse graph).

Assume we want to be able to quickly find all the neighbors of a given node in G. Which of the following representations for this graph would support this operation in the most computationally efficient way?

Question

Consider a graph G with n nodes and m edges, where n >> m (i.e. G is a sparse graph).

Assume we want to be able to quickly find all the neighbors of a given node in G. Which of the following representations for this graph would support this operation in the most computationally efficient way?

BlackTom AI · Accepted Answer

The problem asks which graph representation allows quickly finding all neighbors of a given node in a sparse graph where n >> m.
First, I note that the provided data indicates the correct answer is adjacency list, but the actual list of answer options is missing from the input, so I cannot comment on other choices or map them to option labels.
In general, adjacency list representations store for each node the direct neighbors as a list or set. This means that retrieving all neighbors of a node v requires time proportional to its degree deg(v), plus the overhead of accessing the list for v. In sparse graphs, where the average degree is low, this is highly efficient because you only traverse the small list of neighbors rather than inspecting many non-neighbor candidates.
By contrast, an adjacency matrix would store a 0/1 entry for every possible edge, taking O(n^2) space and requiring O(n) time to scan a row to obtain all neighbors, which is inefficient for large n and sparse graphs, since you would inspect many non-edges.
Other representations not shown here might offer various trade-offs, but for the operation of listing all neighbors quickly in a sparse graph, the adjacency list is the standard optimal choice due to its linear-in-degree access pattern and space efficiency.
If there were multiple options, we would evaluate each by the time complexity of listing neighbors, the space requirements, and how well they scale with sparse connectivity; however, without the other options provided, we can still justify adjacency lists as the preferred representation for fast neighbor enumeration in sparse graphs.

CPSC_V 320 201/202/203 2024W2 Reading Quiz #3 (Graphs)

Consider a graph G with n nodes and m edges, where n >> m (i.e. G is a sparse graph). Assume we want to be able to quickly find all the neighbors of a given node in G. Which of the following representations for this graph would support this operation in the most computationally efficient way?

查看解析

登录即可查看完整答案

类似问题

Graph ADT_5 For a given graph g : We are implementing the following graph using the data structure shown below: adj = { 'u': {'v': 'e', 'w': 'g'}, 'v': {'u': 'e', 'w': 'f'}, 'w': {'u': 'g', 'v': 'f', 'z': 'h'}, 'z': {'w': 'h'}} This graph is implemented using an Adjacency Matrix representation.

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单