Abstract.The maximum weight independent set problem for a general graph is NP-hard. But for some special classes of graphs, polynomial time algorithms do exist for solving it. Based on the divideand-conquer strategy, Pawagi has presented an O(IVIlog[ VI) time algorithm for solving this problem on a tree. In this paper, we propose an O(IVI) time algorithm to improve Pawagi's result. The proposed algorithm is based on the dynamic programming strategy and is time optimal within a constant factor.

N R e G = superficial gas Reynolds number N R e L = superficial liquid Reynolds number R = pipe radius, in. 0, 00 z 8 = film thickness, in.8 p L = liquid density, lb./cu.ft. Subscripts and Superscripts exp pie 1 = coordinate position 2 bar tick = axial velocity of the film, ft./sec. = circumferential velocity of the film, ft./sec. = coordinate direction parallel to the pipe axis positive direction is downstream, in. = angular direction, 0 deg. at the top of the pipe, 180 deg. at the bottom of the pipe, deg. or rad. = experimentally determined value of a variable = value of a variable calculated from a proposed model = coordinate position where 2 is greater than 1 = average value of a variable with respect to a co-= instantaneous value of a variable ordinate direction LITERATURE CITED1. Alexander, L. G., and C. L. Coldren, Ind. Eng. Chem., 43, 1325 (1951).

Abstract| In this paper, a Fiduccia-Mattheyses (FM) algorithm incorporating a novel initial partition generating method is proposed. The proposed algorithm applies to both bipartitioning and multi-way partitioning problems with or without replication. The initial partition generating method is based on a gradient decent algorithm. On partitioning without replication, our algorithm achieves an average of 17% improvement o v er the analytical method, PARABOLI, on bipartitioning, 10% better than Primal Dual method on 4-way partitioning and 51% better than net-based method. On partitioning allowing replication, our algorithm achieves an average of 23% improvement o v er the directed Fiduccia-Mattheyses algorithm on Replication Graph (FMRG) method on bipartitioning.

ABSTRACT

difference between normal dew point and normal boiling point, dimensionless, Tlb -T,/ 8,,,, = corrected temperature param-B = pressure ratio dimensionless, Td-Ta eter, &A8 P d p ' , less, T,/T', T = temperature ratio, dimension-