NACA Technical Reports

"The theory of the hydraulic analogy -- that is, the analogy between water flow with a free surface and two-dimensional compressible gas flow -- and the limitations and conditions of the analogy are discussed. A test was run using the hydraulic analogy as applied to the flow about circular cylinders of various diameters at subsonic velocities extending into the supercritical range. The apparatus and techniques used in this application are described and criticized" (p. 311)

NACA Technical Notes

From Introduction: "The development of the measuring apparatus and techniques is presented herein. The application of the analogy to flows through nozzles and about circular cylinders at subsonic velocities extending into supercritical range is also presented.

On the Sum-of-Squares Algorithm for Bin Packing

In this paper we present a theoretical analysis of the deterministic on-line Sum of Squares algorithm (SS) for bin packing, introduced and studied experimentally in [8], along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time O(nB). It performs remarkably well from an average case point of view: For any discrete distribution in which the optimal expected waste is sublinear, SS also has sublinear expected waste. For any discrete distribution where the optimal expected waste is bounded, SS has expected waste at most O(log n). In addition, we present a randomized O(nB log B)-time on-line algorithm SS , based on SS, whose expected behavior is essentially optimal for all discrete distributions. Algorithm SS also depends on a new linear-programming-based pseudopolynomial-time algorithm for solving the NP-hard problem of determining, given a discrete distribution F , just what is the growth rate for the optimal expected waste. An off-line randomized variant SS performs well in a worst-case sense: For anylistL of integer-sized items to be packed into bins of a fixed size B, the expected number of bins used by SS is at most OPT(L)+ p OPT(L)

On the sum-of-squares algorithm for bin packing

In this paper we present a theoretical analysis of the on-line Sum-of-Squares algorithm (SS) for bin packing along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time O(nB). It performs remarkably well from an average case point of view: For any discrete distribution in which the optimal expected waste is sublinear, SS also has sublinear expected waste. For any discrete distribution where the optimal expected waste is bounded, SS has expected waste at most O(log n). We also discuss several interesting variants on SS, including a randomized O(nB log B)-time on-line algorithm SS ∗ whose expected behavior is essentially optimal for all discrete distributions. Algorithm SS ∗ depends on a new linear-programmingbased pseudopolynomial-time algorithm for solving the NP-hard problem of determining, given a discrete distribution F, just what is the growth rate for the optimal expected waste