Abstract. We consider problems of packing an arbitrary collection of rectangular pieces into an open-ended, rectangular bin so as to minimize the height achieved by any piece. This problem has numerous applications in operations research and studies of computer operation. We devise efficient approximation algorithms, study their limitations, and derive worst-case bounds on the performance of the packings they produce.Key words, two-dimensional packing, bin packing, resource constrained scheduling 1. Introduction. Efficiently packing sets of rectangular figures into a given rectangular area is a problem with widespread application in operations research. Thus, one is inclined to attribute the scarcity of results on this problem, and others of its type, to inherent difficulty rather than to lack of importance. Motivated by the intractability of these problems, we define and analyze certain approximation algorithms. These algorithms are natural in the sense that they would probably be among the first to occur to anyone wishing to design simple, fast procedures for determining easily computed packings. The analysis of these algorithms leads to bounds on the performance of approximate packings relative to the best achievable.

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A problem of increasing importance in the design of large multiprogramming systems is the, so-called, deadlock or deadly-embrace problem. In this arliele we survey the work that has been done on the treatment of deadlocks from bolh the theoretical and practical points of view.

Sequencing to minimize mean finishing time (or mean time in system) is not only desirable to the user, but it also tends to minimize at each point in time the storage required to hold incomplete tasks. In this paper a deterministic model of independent tasks is introduced and new results are derived which extend and generalize the algorithms known for minimizing mean finishing time. In addition to presenting and analyzing new algorithms it is shown that the most general mean-finishing-time problem for independent tasks is polynomial complete, and hence unlikely to admit of a non-enumerative solution.