Multicomputer systems achieve high performance by utilizing a number of com
puting nodes. Recently, by achieving significant reductions in communicatio
n delay, the three-dimensional (3D) torus has emerged as a new candidate in
terconnection topology for message-passing multicomputer systems. In this p
aper, we propose an efficient processor allocation scheme-scan search schem
e-for the 3D torus based on a first-fit approach. The scan search scheme mi
nimizes the average allocation time for an incoming task by effectively man
ipulating the 3D information on a torus as 2D information using a data stru
cture called the CST (Coverage Status Table). Comprehensive computer simula
tion reveals that the allocation time of the scan search scheme is always s
maller than that of the earlier scheme based on a best-fit approach. The di
fference gets larger as the input load increases, and it is as much a facto
r of 3 for high load. To investigate the performance of the proposed scheme
in different scheduling environments, we also consider a non-FCFS scheduli
ng policy along with the typical FCFS policy. The allocation time complexit
y of the scan search scheme is O((LWH2)-H-2). This is significantly smaller
than that of the existing scheme which is O((LWH4)-W-4-H-4). Here, L, W, a
nd H represent the length, width, and height of 3D torus, respectively.