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

Electronic structure and carrier transfer in B-DNA monomer polymers and dimer polymers: Stationary and time-dependent aspects of wire model vs. extended ladder model

We employ two Tight-Binding (TB) approaches to study the electronic structure and hole or electron transfer in B-DNA monomer polymers and dimer polymers made up of $N$ monomers (base pairs): (I) at the base-pair level, using the on-site energies of base pairs and the hopping integrals between successive base pairs, i.e., a wire model and (II) at the single-base level, using the on-site energies of the bases and the hopping integrals between neighboring bases, i.e., an \textit{extended} ladder model since we also include diagonal hoppings. We solve a system of $MD$ ("matrix dimension") coupled equations [(I) $MD$ = $N$, (II) $MD$ = $2N$] for the time-independent problem, and a system of $MD$ coupled $1^\text{st}$ order differential equations for the time-dependent problem. We study the HOMO and the LUMO eigenspectra, the occupation probabilities, the Density of States (DOS) and the HOMO-LUMO gap as well as the mean over time probabilities to find the carrier at each site [(I) base pair or (II) base)], the Fourier spectra, which reflect the frequency content of charge transfer (CT) and the pure mean transfer rates from a certain site to another. The two TB approaches give coherent, complementary aspects of electronic properties and charge transfer in B-DNA monomer polymers and dimer polymers.Comment: 20 pages, 23 figure

Polyvalent Parallelizations for Hierarchical Block Matching Motion Estimation

Block matching motion estimation algorithms are widely used in video coding schemes. In this paper,we design an efficient hierarchical block matching motion estimation (HBMME) algorithm on a hypercube multiprocessor. Unlike systolic array designs, this solution is not tied down to specific values of algorithm parameters and thus offers increased flexibility. Moreover, the hypercube network can efficiently handle the non regular data flow of the HBMME algorithm. Our techniques nearly eliminate the occurrence of “difficult” communication patterns, namely many-to-many personalized communication, by replacing them with simple shift operations. These operations have an efficient implementation on most of interconnection networks and thus our techniques can be adapted to other networks as well. With regard to the employed multiprocessor we make no specific assumption about the amount of local memory residing in each processor. Instead, we introduce a free parameter S and assume that each processor has O(S) local memory. By doing so, we handle all the cases of modern multiprocessors, that is fine-grained, medium-grained and coarse-grained multiprocessors and thus our design is quite general

Προσομοιώσεις Monte Carlo Κλασικού Σιδηρομαγνήτη Heisenberg σε Πλέγματα Κυβικής Συμμετρίας

Μελετήθηκε η συνεχής αλλαγή φάσης για τον κλασικό O(3) σιδηρομαγνήτη Heisenberg σε sc, bcc και fcc πλέγματα. Εφόσον για το συγκεκριμένο πρότυπο δεν υπάρχει διαθέσιμη αναλυτική λύση στις τρεις διαστάσεις, τα χαρακτηριστικά της κρίσιμης συμπεριφοράς μελετήθηκαν: I. Ποιοτικά, στα πλαίσια της προσέγγισης μέσου πεδίου (mean field approximation), με αριθμητικό προσδιορισμό των σημαντικότερων θερμοδυναμικών μεγεθών, μέσω επίλυσης της αυτοσυνεπούς εξίσωσης για τη μαγνήτιση του συστήματος. II. Ποσοτικά, αξιοποιώντας τη μέθοδο προσομοίωσης Monte Carlo, σε συνδυασμό με τη θεωρία κλιμάκωσης πεπερασμένου μεγέθους (finite size scaling) και την υπολογιστική μέθοδο επαναπροσδιορισμού του ενός ιστογράμματος (single histogram reweighting method). Οι κρίσιμοι εκθέτες ν και γ υπολογίστηκαν μελετώντας την κλιμάκωση θερμοδυναμικών μεγεθών από προσομοιώσεις στην κρίσιμη περιοχή κάθε διαφορετικού τύπου πλέγματος. Η κρίσιμη θερμοκρασία μετάβασης εκτιμήθηκε με τη μέθοδο τομής των συσσωρευτών (cumulant crossing method) και με τη μελέτη της κλιμάκωσης των ψευδοκρίσιμων θερμοκρασιών διαφορετικών θερμοδυναμικών ποσοτήτων. Ειδικά στην περίπτωση του sc, προσδιορίστηκε επιπρόσθετα και ο κρίσιμος εκθέτης β, μελετώντας την κλιμάκωση της μαγνήτισης ανά spin στο εκτιμώμενο κρίσιμο σημείο. Οι υπόλοιποι εκθέτες προσδιορίστηκαν έμμεσα, μέσω των νόμων κλιμάκωσης για κάθε τύπο πλέγματος. Τα αποτελέσματα τόσο των κρίσιμων σημείων, όσο και των κρίσιμων εκθετών, βρίσκονται σε συμφωνία με αντίστοιχες μελέτες προσομοιώσεων Monte Carlo και μεθόδων ανάπτυξης σε σειρές, στα πλαίσια των υπολογιζόμενων σφαλμάτων. Επιπλέον, τα αριθμητικά αποτελέσματα που αφορούν τους κρίσιμους εκθέτες στα sc, bcc και fcc πλέγματα, συμφωνούν μεταξύ τους, γεγονός που επιβεβαιώνει τα οικουμενικά χαρακτηριστικά της κρίσιμης συμπεριφοράς.In this thesis the continuous phase transition of the classical O(3) Heisenberg ferromagnet was studied in sc, bcc and fcc lattices. Since no analytical solution is available in three dimensions for this model, the critical behavior was studied: I. Qualitatively, via numerical calculations of the self consistent equation for the magnetization and other important thermodynamic quantities, in the context of the mean field approximation. II. Quantitatively, by making use of Monte Carlo simulations, the finite size scaling theory and the single histogram reweighting method. The critical exponents ν and γ were calculated by studying the scaling properties of various thermodynamic quantities from simulations covering the critical region of each lattice type. The critical temperature was estimated via the cumulant crossing method and the scaling properties of pseudocritical transition points of various thermodynamic quantities. Moreover, in the case of sc lattice, the critical exponent β was determined from the scaling behavior of magnetization per spin in the estimated critical point. The other critical exponents were extracted indirectly, by means of scaling laws for each lattice type. Both the results for the estimated transition points and the critical exponents, are in good agreement with other Monte Carlo studies and series expansion methods with respect to the calculated errors. Furthermore, the values of critical exponents for sc, bcc and fcc lattices agree with each other, which verifies the universal aspects of critical behavior

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

Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games

Additively separable hedonic games and fractional hedonic games have received considerable attention. They are coalition forming games of selfish agents based on their mutual preferences. Most of the work in the literature characterizes the existence and structure of stable outcomes (i.e., partitions in coalitions), assuming that preferences are given. However, there is little discussion on this assumption. In fact, agents receive different utilities if they belong to different partitions, and thus it is natural for them to declare their preferences strategically in order to maximize their benefit. In this paper we consider strategyproof mechanisms for additively separable hedonic games and fractional hedonic games, that is, partitioning methods without payments such that utility maximizing agents have no incentive to lie about their true preferences. We focus on social welfare maximization and provide several lower and upper bounds on the performance achievable by strategyproof mechanisms for general and specific additive functions. In most of the cases we provide tight or asymptotically tight results. All our mechanisms are simple and can be computed in polynomial time. Moreover, all the lower bounds are unconditional, that is, they do not rely on any computational or complexity assumptions

Tight approximation bounds for combinatorial frugal coverage algorithms

We consider the frugal coverage problem, an interesting variation of set cover defined as follows. Instances of the problem consist of a universe of elements and a collection of sets over these elements; the objective is to compute a subcollection of sets so that the number of elements it covers plus the number of sets not chosen is maximized. The problem was introduced and studied by Huang and Svitkina (Proceedings of the 29th IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS), pp. 227–238, 2009) due to its connections to the donation center location problem. We prove that the greedy algorithm has approximation ratio at least 0.782, improving a previous bound of 0.731 in Huang and Svitkina (Proceedings of the 29th IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS), pp. 227–238, 2009). We also present a further improvement that is obtained by adding a simple corrective phase at the end of the execution of the greedy algorithm. The approximation ratio achieved in this way is at least 0.806. Finally, we consider a packing based algorithm that uses semi-local optimization, and show that its approximation ratio is not less than 0.872. Our analysis is based on the use of linear programs which capture the behavior of the algorithms in worst-case examples. The obtained bounds are proved to be tight