  The Coalition Formation with Spatial and Temporal constraints Problem (CFSTP)
is a multi-agent task scheduling problem where the tasks are spatially
distributed, with deadlines and workloads, and the number of agents is
typically much smaller than the number of tasks, thus the agents have to form
coalitions in order to maximise the number of completed tasks. The current
state-of-the-art CFSTP solver, the Coalition Formation with Look-Ahead (CFLA)
algorithm, has two main limitations. First, its time complexity is exponential
with the number of agents. Second, as we show, its look-ahead technique is not
effective in real-world scenarios, such as open multi-agent systems, where new
tasks can appear at any time. In this work, we study its design and define an
extension, called Coalition Formation with Improved Look-Ahead (CFLA2), which
achieves better performance. Since we cannot eliminate the limitations of CFLA
in CFLA2, we also develop a novel algorithm to solve the CFSTP, the first to be
anytime, efficient and with provable guarantees, called Cluster-based Coalition
Formation (CCF). We empirically show that, in settings where the look-ahead
technique is highly effective, CCF completes up to 30% (resp. 10%) more tasks
than CFLA (resp. CFLA2) while being up to four orders of magnitude faster. Our
results affirm CCF as the new state-of-the-art algorithm to solve the CFSTP.
