# The Least Cost Directed Perfect Awareness Problem - Benchmark Instances and Solutions

## Description

This dataset contains complementary data to the paper "The Least Cost Directed Perfect Awareness Problem: Complexity, Algorithms and Computations" [1]. Here, we make available two sets of instances of the combinatorial optimization problem studied in that paper, which deals with the spread of information on social networks. We also provide the best known solutions and bounds obtained through computational experiments for each instance. The first input set includes 300 synthetic instances composed of graphs that resemble real-world social networks. These graphs were produced with a generator proposed in [2]. The second set consists of 14 instances built from graphs obtained by crawling Twitter [3]. The directories "synthetic_instances" and "twitter_instances" contain files that describe both sets of instances, all of which follow the format: the first two lines correspond to: <n> <m> where <n> and <m> are the number of vertices and edges in the graph. Each of the next <n> lines contains: <v> <c> <t> where <v> identifies a vertex while <c> and <t> are the cost and threshold associated to that vertex. Each of the <m> remaining lines contains: <u> <v> <w> where <u> and <v> identify an ordered pair of vertices that determines a directed edge with weight <w>. The directories "solutions_for_synthetic_instances" and "solutions_for_twitter_instances" contain files that describe the best known solutions for both sets of instances, all of which follow the format: the first line corresponds to: <s> where <s> is the number of vertices in the solution. Each of the next <s> lines contains: <v> where <v> identifies a seed vertex. The last line contains: <c> where <c> is the solution cost. Lastly, two files, namely, "bounds_for_synthetic_instances.csv" and "bounds_for_twitter_instances.csv", enumerate the values of the best known lower and upper bounds for both sets of instances. This work was supported by grants from Santander Bank, Brazil. Caveat: the opinions, hypotheses and conclusions or recommendations expressed in this material are the responsibility of the authors and do not necessarily reflect the views of Santander. References [1] F. C. Pereira, P. J. de Rezende. The Least Cost Directed Perfect Awareness Problem: Complexity, Algorithms and Computations. Submitted. 2023. [2] B. Bollobás, C. Borgs, J. Chayes, and O. Riordan. Directed scale-free graphs. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’03, pages 132–139, 2003. [3] C. Schweimer, C. Gfrerer, F. Lugstein, D. Pape, J. A. Velimsky, R. Elsässer, and B. C. Geiger. Generating simple directed social network graphs for information spreading. In Proceedings of the ACM Web Conference 2022, WWW ’22, pages 1475–1485, 2022.

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## Funding

Santander Bank, Brazil