Space-Efficient Parallel Algorithms for Combinatorial Search Problems

We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound, both involving the visit of an $n$-node tree of height $h$ under the assumption that a node can be accessed only through its father or its children. For both problems we propose efficient algorithms that run on a $p$-processor distributed-memory machine. For backtrack search, we give a deterministic algorithm running in $O(n/p+h\log p)$ time, and a Las Vegas algorithm requiring optimal $O(n/p+h)$ time, with high probability. Building on the backtrack search algorithm, we also derive a Las Vegas algorithm for branch-and-bound which runs in $O((n/p+h\log p \log n)h\log^2 n)$ time, with high probability. A remarkable feature of our algorithms is the use of only constant space per processor, which constitutes a significant improvement upon previous algorithms whose space requirements per processor depend on the (possibly huge) tree to be explored.Comment: Extended version of the paper in the Proc. of 38th International Symposium on Mathematical Foundations of Computer Science (MFCS

bcl-2 in normal human breast and carcinoma, association with oestrogen receptor-positive, epidermal growth factor receptor-negative tumours and in situ cancer.

The role of bcl-2 expression in solid tumours is as yet undefined. It was, therefore, the purpose of this study to investigate expression of bcl-2 protein in 111 human breast carcinomas using immunohistochemistry and the monoclonal antibody bcl-2 124. Expression was then compared with the established indicators of prognosis and biological behaviour in malignant breast disease. No relationship could be observed between bcl-2 and node status, tumour size, differentiation, type or age at excision. However, a strong positive relationship was seen between bcl-2 and oestrogen receptor (ER), with 70 of 88 (80%) bcl-2-positive tumours being ER positive also, compared with seven of 23 (30%) bcl-2-negative tumours being ER positive (P < 0.0001). The converse was found when bcl-2 was compared with epidermal growth factor receptor (EGFR). A strong negative relationship was observed, with 26 of 88 (30%) bcl-2-positive tumours being EGFR positive, compared with 16 of 23 (70%) bcl-2-negative tumours being EGFR positive (P = 0.001), raising the possibility that bcl-2 is an ER-regulated gene. An inverse relationship was also found between bcl-2 and the oncogenes c-erbB-2 and p53. Thus, loss of bcl-2 expression in breast cancer is associated with a range of molecular markers of poor prognosis and may define part of an ER-negative, EGFR-positive phenotype

Loss of antigen-presenting molecules (MHC class I and TAP-1) in lung cancer.

Presentation of endogenous antigenic peptides to cytotoxic T lymphocytes is mediated by the major histocompatibility complex (MHC) class I molecules. For the stable assembly of MHC class I complex it is necessary that the antigenic peptide is transported by the MHC-encoded transporters TAP-1 and TAP-2 into a pre-Golgi region. T-cell-mediated host-vs-tumour response might therefore depend on the presence of these molecules on tumour cells. The presence of MHC class I antigens and TAP-1 was studied in a series of 93 resection specimens of non-small-cell lung carcinomas (NSCLCs) by immunohistochemical methods using antibodies against the assembled class I molecule, beta 2-microglobulin (beta 2-m), heavy-chain A locus, A2 allele and TAP-1 protein. Eighty-six patients were included in the survival analysis. Total loss of class I molecule was observed in 38% of the cases and was usually accompanied by loss of beta 2-m and of heavy chain A locus. Selective loss of A locus was seen in 8.3% and of A2 allele in 27% of the cases. TAP-1 loss was always combined with beta 2-m and/or heavy chain A locus loss. No correlation was found between the expressional status of any of the above molecules, including the selective A2 allelic loss and histological type, degree of differentiation, tumoral stage, nodal stage and survival. Our findings suggest that loss of antigen-presenting molecules (including both MHC class I alleles and TAP-1) is a frequent event in lung cancer. However, the immunophenotypic profile of MHC class I and TAP-1 seems to be unrelated in vivo to the phenotype, growth or survival of NSCLC