In this paper we have introduced the K1 heuristic algorithm for dynamic task scheduling with precedence constraints and communication delays. The execution of a task set repeats in cycles, while the execution and communication profile of a task set changes in time. During a task set execution, a new schedule is generated by tuning the previous schedule. The scheduling is distributed - performed on the processors of a highly parallel computer architecture. The goal is to reduce a dominant sequence of a task set during run-time. Only the tasks that can have an influence on dominant sequence reduction are considered for reordering/migration. The applied techniques are load balancing, task reordering, and data-wait reduction. Simulation is used for the algorithm validation and evaluation.