### Table 1: Multisets Used by the Algorithm

1995

"... In PAGE 2: ... The multiset of all measured is called M. See Table1 and Figure 1. The collection of fragments whose lengths are assigned to X or Y can be used to locate markers.... In PAGE 5: ...2 The Cost of a Partial Assignment For a partial assignment let N; X; Y; and B be the multisets of already assigned lengths and let Z be those lengths not yet assigned. If the partial assignment (N; X; Y; B; Z) is to lead to a good complete assignment, the multiset M must contain data similar to that in the multiset of computed fragment lengths C (see Table1 ). In particular, if jCj gt; jMj then the partial assignment cannot lead to a... ..."

Cited by 1

### Table 4 Number of distinguishers returned by the setcover greedy algorithm (SGA) and the multi-step rounding algorithm in [2] (RND) for varying redundancy and number of sequences. For each value of n we report the average over 10 testcases, each consisting of n random sequences of length 1,000. Boldface entries correspond to instances for which the multi-step rounding algorithm has better solution quality than setcover greedy. Algorithm r n = 10 n = 20 n = 50 n = 100 n = 200

2005

"... In PAGE 15: ... Finally, if the selected set of distinguishers is not yet feasible, add further distinguishers using the setcover greedy algorithm The approximation guarantee established in [2] for the general set multicover problem translates into an approximation factor of 2 ln n ln r for robust string barcoding with redundancy r, which suggests that the multi-step rounding algorithm is likely to improve upon the setcover greedy for high redundancy constraints. Table4 gives the results of experiments comparing the setcover greedy and multi-step rounding algorithms on testcases con- sisting of up to 200 random sequences, each of length 1,000 for redundancy requirement ranging from 1 to 300. The results con rm that the multi-step rounding algorithm has better solution quality than setcover greedy when redundancy requirement is large relative to the number of sequences (entries typeset in boldface), yet the setcover greedy has best performance for most practical redundancy requirements.... ..."

Cited by 7

### Table 7. Upper multi-set bounds

1998

"... In PAGE 28: ... Table 6. Upper and lower integer bounds Place Upper Bound Lower Bound NextSend 1 1 ReceiveAck 1 1 Send 1 1 Sending 1 0 TransmitData 1 1 Waiting 1 0 NextReceive 1 1 ReceiveData 1 1 Received 1 1 TransmitAck 1 1 Table7 shows the upper multi-set bounds for the places in the sender. By de nition, the upper multi-set bound of a place is the smallest multi-set which is larger than all reachable markings of the place.... ..."

Cited by 61

### Table 2: Performance of exact algorithm

"... In PAGE 16: ...ore on this in section 5.4.1. A nal issue to consider is whether the problems in Table 3 are somehow \easy. quot; We would argue that the numbers in Table2 show otherwise. In any case, consider problem MS5.... ..."

### Table 1. Comparison of the Multiset Hash Functions

2003

"... In PAGE 11: ...Conclusion We have introduced incremental multiset hash functions which can be efficiently updated, and for which the ordering of inputs is not important. Table1 sum- marizes our comparison of the multiset hash functions introduced in this paper. In the table, we indicate whether the security is based on pseudorandom family of hash functions (PRF), the random oracle model (RO), the discrete log as- sumption (DL), or/and the hardness of the worst case shortest vector problem (SV).... ..."

Cited by 18

### Table 2: Comparison of exact algorithms

1998

"... In PAGE 5: ... In a second series of experiments we applied our algo- rithm to a larger set of benchmark circuits from LGSynth93. The results are given in Table2 . As can easily be seen our algorithm is much faster in most cases #28see e.... ..."

Cited by 28

### Table 2: Comparison of exact algorithms

1998

"... In PAGE 5: ... In a second series of experiments we applied our algo- rithm to a larger set of benchmark circuits from LGSynth93. The results are given in Table2 . As can easily be seen our algorithm is much faster in most cases (see e.... ..."

Cited by 28

### Table 2: Comparison of exact algorithms

1998

"... In PAGE 5: ... In a second series of experiments we applied our algo- rithm to a larger set of benchmark circuits from LGSynth93. The results are given in Table2 . As can easily be seen our algorithm is much faster in most cases #28see e.... ..."

Cited by 28

### Table 3. Performance of checking races for transactional Multiset

"... In PAGE 10: ... This commit action was inserted in the synchronization event list where the first lock release in a transaction would have been inserted if we were not explicitly considering transactions. We measured, for different numbers of threads sharing a multi- set of size 10, the runtime with race checking enabled for the trans- actions as described in Sections 4 and 5 ( Table3 ). The table also reports the number of shared variable accesses and the number of transactions in the executions.... ..."

### Table 3. Performance of checking races for transactional Multiset

"... In PAGE 10: ... This commit action was inserted in the synchronization event list where the first lock release in a transaction would have been inserted if we were not explicitly considering transactions. We measured, for different numbers of threads sharing a multi- set of size 10, the runtime with race checking enabled for the trans- actions as described in Sections 4 and 5 ( Table3 ). The table also reports the number of shared variable accesses and the number of transactions in the executions.... ..."