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Serverless computing, in particular the Function-as-a-Service (FaaS) execution model, has recently shown to be effective for running large-scale computations. However, little attention has been paid to highly-parallel applications with unbalanced and irregular workloads. Typically, these workloads have been kept out of the cloud due to the impossibility of anticipating their computing resources ahead of time, frequently leading to severe resource over- and underprovisioning situations. Our main insight in this article is, however, that the elasticity and ease of management of serverless computing technology can be a key enabler for effectively running these problematic workloads for the first time in the cloud. More concretely, we demonstrate that with a simple serverless executor pool abstraction one can achieve a better cost-performance trade-off than a Spark cluster of static size built upon large EC2 virtual machines. To support this conclusion, we evaluate three irregular algorithms: Unbalanced Tree Search (UTS), Mandelbrot Set using the Mariani-Silver algorithm and Betweenness Centrality (BC) on a random graph. For instance, our serverless implementation of UTS is able to outperform Spark by up to 55% with the same cost. We also show that a serverless environment can outperform a large EC2 in the BC algorithm by a 10% using the same amount of virtual CPUs. This provides the first concrete evidence that highly-parallel, irregular workloads can be efficiently executed using purely stateless functions with almost zero burden on users i.e., no need for users to understand non-obvious system-level parameters and optimizations. Furthermore, we show that UTS can benefit from the FaaS pay-as-you-go billing model, which makes it worth for the first time to enable certain application-level optimizations that can lead to significant improvements (e.g. of 41%) with negligible increase in cost.