4th International Conference on Principles and Practices ... - MADOC

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milliseconds speedup 1.8e+07 1.6e+07 1.4e+07 1.2e+07 1e+07 8e+06 6e+06 4e+06 2e+06 0 Thu Jul 21 22:28:37 2005 16 14 12 10 8 6 4 2 0 GBs of Katsuras example on compute 0 2 4 6 8 10 12 14 16 #CPUs kat_7 computing time kat_7 ideal GBs of Katsuras example on compute 0 2 4 6 8 10 12 14 16 Thu Jul 21 22:28:37 2005 #CPUs kat_7 speedup kat_7 ideal milliseconds speedup 90000 80000 70000 60000 50000 40000 30000 20000 10000 0 0 2 4 6 8 10 12 14 16 Sat Dec 31 19:47:11 2005 16 14 12 10 8 6 4 2 0 GBs of Katsuras example on compute kat_6 computing time kat_6-old computing time kat_6 ideal #CPUs 0 2 4 6 8 10 12 14 16 Sat Dec 31 19:47:11 2005 GBs of Katsuras example on compute #CPUs kat_6 speedup kat_6-old speedup kat_6 ideal Figure 6: Katsura 7 parallel Groebner base, 16 CPU JDK 1.4, 32 bit JVM, option UseParallelGC, Intel XEON 2.7 GHz, 1GB JVM memory, 0 CPUs means sequential Figure 8: Katsura 6 parallel Groebner base, 16 CPU JDK 1.4, 32 bit JVM, option UseParallelGC, Intel XEON 2.7 GHz, 1GB JVM memory, 0 CPUs means sequential milliseconds speedup 1.1e+07 1e+07 9e+06 8e+06 7e+06 6e+06 5e+06 4e+06 3e+06 2e+06 1e+06 GBs of Katsuras example on rumtest7 0 1 2 3 4 5 6 7 8 Thu Feb 02 11:04:29 2006 9 8 7 6 5 4 3 2 1 0 katsura_7 computing time katsura_7 ideal #CPUs GBs of Katsuras example on rumtest7 0 1 2 3 4 5 6 7 8 Thu Feb 02 11:04:29 2006 #CPUs katsura_7 speedup katsura_7 ideal Figure 7: Katsura 7 parallel Groebner base, 8 CPU JDK 1.5, 64 bit JVM, AMD Opteron 2.2 GHz, 1GB JVM memory, 0 CPUs means sequential version tween powers of variables are computed, e.g. x e j j ∗ x e i c i ′ j ′xe i i xe j j + p i ′ j ′ for some i, j. These new relations are then used to speedup future non commutative multiplications. GenSolvablePolynomial implements the non commutative multiplication and uses the additive commutative methods from its super class. As mentioned before, casts are required for the super class methods, e.g. (GenSolvablePolynomial) p.sum(q). i = The respective objects are however correctly build using the methods from the solvable ring factory. The class design allows solvable polynomial objects to be used in all algorithms where GenPolynomials can be used as parameters as long as no distinction between left and right multiplication is required. 4.1 Groebner bases As an application of the generic polynomials we have implemented some more advanced algorithms. E.g. polynomial reduction (a kind of multivariate polynomial division algorithm) or Buchbergers algorithm to compute Groebner bases (a kind of a Gaussian elimination for multivariate polynomials). The algorithms are also implemented for solvable polynomial rings (with left, right and two-sided variants) and modules over these rings. These algorithms are implemented following standard object oriented patterns (see figure 5). There is an interface, e.g. GroebnerBase, which specifies the desirable functionality, like isGB(), GB() or extGB(). Then there is an abstract class, e.g. Groebner- BaseAbstr, which implements as much methods as possible. It further defines the desirable constructor parameters, e.g. a Reduction parameter which sets a polynomial reduction engine with suitable properties. Finally there are concrete classes which extend the abstract class and implement different algorithmic details. E.g. GroebnerBaseSeq implements a sequential, GroebnerBaseParallel implements a thread parallel and GroebnerBaseDistributed implements a network distributed version of the core Groebner base algorithm. In 2003 we compared the Groebner base algorithm to a similar version and implementation of MAS [13]. For the big Trinks example the Java implementation was 8 times faster. 4.2 Parallelism During the work on [14] we developed the ideas for design of parallel and distributed implementation of core algorithms. The Groebner base computation is done by a variant of the classical Buchberger algorithm. It maintains a data structure, called pair list, for book keeping of the computations (forming S-polynomials and doing reductions). This data structure is implemented by CriticalPairList and OrderedPairList. Both have synchronized methods put() and getNext() respectively removeNext() to update the data structure. In this way the pair list is used as work queue in the parallel and distributed implementations. The parallel implementations scales well for up to 8 CPUs, for a well structured problem (figures 6 and 7) and up to 4 CPUs on a smaller problem (figure 8). Since the polynomials are implemented as immutable classes no further synchronization is required for the polynomial methods. The distributed implementation makes further use of a distributed list (im- 151
plemented via a distributed hash table DHT) for the communication of the reduction bases and a distributed thread pool for running the reduction engines in different computers. Java object serialization is used to encode polynomials for network transport. Polynomials are only transfered once to or from a computing node, critical pairs are only transfered using indexes of polynomials in the DHT. 5. CONCLUSIONS We have provided a sound object oriented design and implementation of a library for algebraic computations in Java. For the first time we have produced a type safe library using generic type parameters. The proposed interfaces and classes are as expressive as the category and domain constructs of Axiom or Aldor, although we have not jet implemented all possible structures. The library provides multivariate polynomials and multiprecision base coefficients which are used for a large collection of Groebner base algorithms. For the first time we have presented an object oriented implementation of non-commutative solvable polynomials and many non-commutative Groebner base algorithms. The library employs various design patterns, e.g. creational patterns (factory and abstract factory) for algebraic element creation. For the main working structures we use the Java collection framework. The parallel and distributed implementation of Groebner base algorithms draws heavily on the Java packages for concurrent programming and internet working. The suitability of the design is exemplified by the successful implementation of a large part of ‘additive ideal theory’, e.g. different Groebner base and syzygy algorithms. With the Jython wrapper the library can also be used interactively. We hope that the problems with type erasure in generic interfaces could be solved in some future version of the Java language. It would also be helpful if there was some way to impose restrictions on constructors in interface definitions. In the future we will implement more of ‘multiplicative ideal theory’, i.e. multivariate polynomial greatest common divisors and factorization. Acknowledgments I thank Thomas Becker (who is working or thinking about a C++ implementation of a polynomial template library) for discussions on the subject. Further I thank Aki Yoshida from whom I learned much about object oriented programming and design. Thanks also to the anonymous referees for the suggestions to improve the paper. 6. REFERENCES [1] M. Y. Becker. Symbolic Integration in Java. PhD thesis, Trinity College, University of Cambridge, 2001. [2] T. Becker and V. Weispfenning. Gröbner Bases - A Computational Approach to Commutative Algebra. Springer, Graduate Texts in Mathematics, 1993. [3] L. Bernardin, B. Char, and E. Kaltofen. Symbolic computation in Java: an appraisement. In S. Dooley, editor, Proc. ISSAC 1999, pages 237–244. ACM Press, 1999. [4] M. Bronstein. Sigma it - a strongly-typed embeddable computer algebra library. In J. Calmet and C. Limongelli, editors, Proc. DISCO 1996, volume 1128 of Lecture Notes in Computer Science, pages 22–33. Springer, 1996. [5] J. Buchmann and T. Pfahler. LiDIA, pages 403–408. in Computer Algebra Handbook, Springer, 2003. [6] M. Conrad. The Java class package com.perisic.ring. Technical report, http://ring.perisic.com/, 2002-2004. [7] D. Cox, J. Little, and D. O’Shea. Ideals, Varieties and Algorithms. Springer, Undergraduate Texts in Mathematics, 1992. [8] J. Grabmaier, E. Kaltofen, and V. Weispfenning, editors. Computer Algebra Handbook. Springer, 2003. [9] G.-M. Greuel, G. Pfister, and H. Schönemann. Singular - A Computer Algebra System for Polynomial Computations, pages 445–450. in Computer Algebra Handbook, Springer, 2003. [10] R. Jenks and R. Sutor, editors. axiom The Scientific Computation System. Springer, 1992. [11] H. Kredel. A systems perspective on A3L. In Proc. A3L: Algorithmic Algebra and Logic 2005, pages 141–146. University of Passau, April 2005. [12] H. Kredel. The Java algebra system. Technical report, http://krum.rz.uni-mannheim.de/jas/, since 2000. [13] H. Kredel and M. Pesch. MAS: The Modula-2 Algebra System, pages 421–428. in Computer Algebra Handbook, Springer, 2003. [14] H. Kredel and A. Yoshida. Thread- und Netzwerk- Programmierung mit Java. dpunkt, 2nd edition, 2002. [15] V. Niculescu. A design proposal for an object oriented algebraic library. Technical report, Studia Universitatis ”Babes-Bolyai”, 2003. [16] V. Niculescu. OOLACA: an object oriented library for abstract and computational algebra. In J. M. Vlissides and D. C. Schmidt, editors, OOPSLA Companion, pages 160–161. ACM, 2004. [17] A. Platzer. The Orbital library. Technical report, University of Karlsruhe, http://www.functologic.com/, 2005. [18] E. Poll and S. Thomson. The type system of Aldor. Technical report, Computing Science Institute Nijmegen, 1999. [19] P. S. Santas. A type system for computer algebra. J. Symb. Comput., 19(1-3):79–109, 1995. [20] S. Watt. Aldor, pages 265–270. in Computer Algebra Handbook, Springer, 2003. [21] C. Whelan, A. Duffy, A. Burnett, and T. Dowling. A Java API for polynomial arithmetic. In PPPJ ’03: Proceedings of the 2nd international conference on Principles and practice of programming in Java, pages 139–144, New York, NY, USA, 2003. Computer Science Press, Inc. [22] R. Zippel. Weyl computer algebra substrate. In Proc. DISCO ’93, pages 303–318. Springer-Verlag Lecture Notes in Computer Science 722, 2001. 152
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Edited by: Ralf Gitzel, Markus Alek
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Message from the Chairs Dear confer
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Sam Midkiff, Purdue University (USA
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Session F: Novel Uses of Java______
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The Project Maxwell Assembler Syste
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tomated assembler and disassembler
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memory address offset mnemonic argu
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5.2 Instruction Templates The assem
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ange for a very short restart/debug
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Tatoo: an innovative parser generat
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In the grammar file an error termin
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Figure 3: Push parsers and lexers L
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eturn visit((Expr)p1, param); } R v
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Session B Program and Performance A
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Table 1: Use of interfaces and deco
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Table 3: Comparison of the situatio
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will trigger the creation of many n
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Appendix A 10 9 8 7 6 5 4 3 2 1 0 1
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Throughout this paper, we make no a
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instrumented program and obtained t
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Figure 5: Investigation of garbage
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to the same category—again, this
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Investigating Throughput Degradatio
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Figure 1: Apache. Throughput degrad
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Minor GC Full GC Workload # of Avg.
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Figure 6: Comparing memory and pagi
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GenRC on the other hand, allows the
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Session C Mobile and Distributed Sy
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ing a continuous buffer for raw dat
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the data arrival speed is more impo
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public class StreamingClient { publ
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importance of β in our aggregation
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Enabling Java Mobile Computing on t
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A strongly mobile thread has the ab
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a context switch occur. The invoked
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above phases. Now, the new stack ha
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5 frames 15 frames 25 frames Pure d
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Juxta-Cat: A JXTA-based platform fo
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Figure 1: JXTA Architecture. 3. JUX
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• Send a discovery query to the p
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The best candidate is then the one
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Local Hosts=2 Hosts=4 Hosts=8 Hosts
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Session D Resource and Object Manag
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Enterprise Edition (J2EE). It enabl
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As pictured in Figure 4, JDOSecure
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Methods of a PersistenceManager, th
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Datenmodell abstrahiert user role,
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An Extensible Mechanism for Long-Te
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missing object references in the de
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4.2 Mapping the name spaces of the
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Page 123 and 124: 2. FRAMEWORK The Framework for Unif
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Page 129 and 130: 3. FUTURE WORK The ability to split
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Page 183 and 184: The idea of Java 5.0 type inference
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Page 189 and 190: Infinite Streams in Java Dominik Gr
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an error is subsequently generated
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3. BASIC TERMINOLOGY As object-orie
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• subtyping • (implementation)
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Improving the Quality of Programmin
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Results of online checks (shortened
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212
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214
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Experiences With Hierarchy-Based Co
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Sub View Child DataField 0..n Ke
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Figure 8 - Actual State Charts elem
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associations, which may result in r
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M3PS: A Multi-Platform P2P System B
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In following, we will explain in de
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Figure 10. JDP in Windows XP. Figur
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Mapping Clouds of SOA- and Business
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the technical SOA events (from the
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component and the business process
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Figure 13. “Business Value of Dat
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Solaris of SUN. This platform provi
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status change of an application is
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coming up, is presently discussing
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ISBN: 3-939352-05-5 ISBN: 978-3-939
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