### Table 4: The di erences of the parallel algorithm from serial SuperLU. Notation Meaning

1999

"... In PAGE 6: ... In order to make the parallel algorithm e cient, we need to make non-trivial modi cations to serial SuperLU. All these changes are summarized in Table4 and discussed in the subsections below. These show that the parallel algorithm is not a straightforward parallelization of the serial one, and illustrate the program complications arising from parallelization.... ..."

Cited by 47

### Table 4: The di erences of the parallel algorithm from serial SuperLU. Notation Meaning

1999

"... In PAGE 6: ... In order to make the parallel algorithm e cient, we need to make non-trivial modi cations to serial SuperLU. All these changes are summarized in Table4 and discussed in the subsections below. These show that the parallel algorithm is not a straightforward parallelization of the serial one, and illustrate the program complications arising from parallelization.... ..."

Cited by 47

### Table 4: The di erences of the parallel algorithm from serial SuperLU. Notation Meaning

1999

"... In PAGE 6: ... In order to make the parallel algorithm e cient, we need to make non-trivial modi cations to serial SuperLU. All these changes are summarized in Table4 and discussed in the subsections below. These show that the parallel algorithm is not a straightforward parallelization of the serial one, and illustrate the program complications arising from parallelization.... ..."

Cited by 47

### Table 4: The di#0Berences of the parallel algorithm from serial SuperLU.

1999

"... In PAGE 6: ... In order to make the parallel algorithm e#0Ecient, we need to make non-trivial modi#0Ccations to serial SuperLU. All these changes are summarized in Table4 and discussed in the subsections below. These show that the parallel algorithm is not a straightforward parallelization of the serial one, and illustrate the program complications arising from parallelization.... ..."

Cited by 47

### Table 1. Parallel algorithm for training CRFs

2006

"... In PAGE 14: ... The skewness is calculated using the entropy-based measure introduced in [14]. Table1 . Parameters settings Database T10I4D100k Number of transactions 100,000 Number of items 100 Average Transaction size 10 Average size of maximal potentially frequent itemsets 4 Node i Outgoing Message CPU Incoming Message incoming Message Candidates List Input Queue Waiting Queue Outgoing Message Database ... In PAGE 40: ... The workers are distributed equally among the clusters. Table1 shows the different configurations of both scenarios. The hierarchical configurations are compared to the centralized approach.... In PAGE 62: ... As a result, the parallelization of the training process is quite straightforward. How the Parallel Algorithm Works The parallel algorithm is shown in Table1 . The algorithm follows the master-slave strategy.... ..."

### Table 6. Axioms for rewriting parallel composition and abstraction.

2001

"... In PAGE 19: ... We present a set of additional laws, that allow one to rewrite parallel composition, as well as abstraction into the basic operators of PAc. Table6 lists the necessary laws. Law (X) is usually called the expansion law.... In PAGE 35: ... One of the consequences of this independent delaying is that the expansion law (X) (cf. Table6 ) can be extended in a rather straightforward way to Interac- tive Markov Chains. Table 13 lists the resulting law, together with an additional law for abstraction, that (together with the ones in Table 6) allow one to rewrite parallel composition, as well as abstraction into the basic operators of IMCc.... In PAGE 35: ... Table 6) can be extended in a rather straightforward way to Interac- tive Markov Chains. Table 13 lists the resulting law, together with an additional law for abstraction, that (together with the ones in Table6 ) allow one to rewrite parallel composition, as well as abstraction into the basic operators of IMCc. Example 21.... ..."

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### Table 8: Runtime (axelrod), varying the number of iterations per match applications,3 the TCP based implementation performs nearly as good as the UDP based im- plementation. The explanation is fairly straightforward though. Really large grain parallel applications exchange messages only rarely. Compared to the total CPU time consumption, the additional overhead of the TCP based implementation per message exchange over the UDP based implementation is small. Since not many messages are exchanged, this overhead does not add up to a signi cant amount. 4.2.3 Summary The experiments show that the new UDP based implementation outperforms the previ- ous TCP based implementation both in terms of CPU time consumption and application runtime. Furthermore, our preliminary results seem to indicate that the UDP based im- plementation scales better to larger networks. For large grain parallel applications, on the other side, the TCP based implementation performs nearly as good as the UDP based implementation.

### Table 13. Axioms for rewriting parallel composition and abstraction on IMCc.

2001

"... In PAGE 35: ... Table 6) can be extended in a rather straightforward way to Interac- tive Markov Chains. Table13 lists the resulting law, together with an additional law for abstraction, that (together with the ones in Table 6) allow one to rewrite parallel composition, as well as abstraction into the basic operators of IMCc. Example 21.... ..."

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### Table 6.7: LGS on two nodes Thus performance degrades with the increasing overhead of supporting additional VPs. In summary, UPVM supports over-decomposition much better than PVM. 6.4 Migration performance Since the main goal of UPVM is to achieve unobtrusive and e cient parallel computation, we use three basic measures in characterizing its performance. These are: 1. Inherent method overhead. How much overhead does an application incur when using UPVM as compared to using a straightforward implementation (i.e., standard PVM) when no migration takes place? That is, what is the overhead of UPVM in the quiet case?

### Table 3: Abstract virtual methods of the parallelBranching and parallelBranchSub classes. overlap in clusters consisting of just one processor. Three run-time parameters, all de ned in parallelPicoBase, govern the partitioning of processors into clusters: clusterSize, numClusters, and hubsDontWorkSize. First PICO nds the size k of a \typical quot; cluster via the formula k = min clusterSize; max

2000

"... In PAGE 35: ... Further, we also de ned a parallel subproblem class parMILPNode with parallelBranchSub and MILPNode as virtual public base classes. We also provided straightforward implementations of the constructors and destructors for these classes, along with the virtual methods described in Table3... ..."

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