You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Literature Survey on Finding Influential Communities in Large Scale Networks 
Chapter Title:  A. Non-containment Community Search 
1. Abstract of Cited Paper (BIB001):  Finding decompositions of a graph into a family of communities is crucial to understanding its underlying structure. Algorithms for finding communities in networks often rely only on structural information and search for cohesive subsets of nodes. In practice however, we would like to find communities that are not only cohesive, but also influential or important. In order to capture such communities, Li, Qin, Yu, and Mao introduced a novel community model called "k-influential community" based on the concept of $k$-core, with numerical values representing "influence" assigned to the nodes. They formulate the problem of finding the top-r most important communities as finding r connected k-core subgraphs ordered by the lower-bound of their importance. In this paper, our goal is to scale-up the computation of top-r, k-core communities to web-scale graphs of tens of billions of edges. We feature several fast new algorithms for this problem. With our implementations, we show that we can efficiently handle massive networks using a single consumer-level machine within a reasonable amount of time. 
2. Abstract of Cited Paper (BIB002):  Community search over large graphs is a fundamental problem in graph analysis. Recent studies propose to compute top-k influential communities, where each reported community not only is a cohesive subgraph but also has a high influence value. The existing approaches to the problem of top-k influential community search can be categorized as index-based algorithms and online search algorithms without indexes. The index-based algorithms, although being very efficient in conducting community searches, need to pre-compute a special-purpose index and only work for one built-in vertex weight vector. In this paper, we investigate on-line search approaches and propose an instance-optimal algorithm LocalSearch whose time complexity is linearly proportional to the size of the smallest subgraph that a correct algorithm needs to access without indexes. In addition, we also propose techniques to make LocalSearch progressively compute and report the communities in decreasing influence value order such that k does not need to be specified. Moreover, we extend our framework to the general case of top-k influential community search regarding other cohesiveness measures. Extensive empirical studies on real graphs demonstrate that our algorithms outperform the existing online search algorithms by several orders of magnitude.

Literature Review:
Following the definition of k-communities, it is possible that an influential k-community is a subgraph of another influential k-community. However, for most of the practical applications, one would prefer to not have such relations present in the output. Thus the problem statement of finding top-r noncontainment influential k-communities was introduced. OnlineAll BIB001 checks for every community generated whether it contains a k-core or not and only those are considered for the final output which have no k-cores present in it. Forward Algorithm BIB002 uses an additional array to store the degree of a node and then used its value to check for non-containment. A slight modification in LocalSearch BIB003 was also suggested in the algorithm to tackle the above task. To summarize we can say that the modified problem statement can be easily solved by providing slight modifications to the existing algorithms.