Results

**1 - 3**of**3**### Table 1: Comparison of Object Location Systems. In this table, n is the number of nodes. For simplicity, we assume that the network diameter is polynomial in n, and that assume the number of objects is O(n). Both stretch and hops refer to an object search. Space assumes that the object IDs occupy a constant number of bytes. Insert cost shows the number of hops or messages needed for node insertion; a - means the system does not provide an algorithm. In RRVV, the number of changes needed is polylogarithmic, but they do not give an algorithm to make the changes. In most cases, the time for insertion is given with high probability. In some cases, various messages can be sent in parallel; we did not allow for this optimization in stating the bounds in this table.

2002

"... In PAGE 2: ...4 Neither of these techniques are guaranteed to find objects. Table1 summarizes related work alongside our contributions. Systems with no entry in the Stretch, Metric column do not con- sider stretch at all; those with special assume the metric space has a certain low-expansion property described in Section 3.... In PAGE 2: ...sed for general metric spaces (i.e., spaces that do not meet the conditions assumed by PRR) to get results similar to those of Awerbuch and Peleg [1]. Table1 gives a summary of some of the previous results along with ours. Note that our result for general metrics can be improved using results of Thorup and Zwick [32] to use only O(n log n) space.... In PAGE 3: ... We also prove that an alternate scheme by Plaxton, Rajaraman, and Richa (called PRR v.0 in Table1 ) gives a low stretch solution for general metric spaces. This follows from arguments similar to those used by Bourgain [4] for metric embeddings.... ..."

Cited by 131

### Table 1: Properties of low{tax vs. high{tax companies

"... In PAGE 4: ... If there was a regime{shift, and rms become pessimistic about the future, and invested less in physical assets, then we would see a resurgence of tax payments in the following years under the same tax regime. 2To the extent that tax incentives for exports and for investment in backward areas have generated low e ective tax rates, the results of Table1 are an incomplete depiction of the extent to which tax evasion is a poor explanation of the low{tax phenomenon. 3Rajaraman and Koshy emphasise the role of maat in improving the e ciency of invest- ment, as opposed to the risk of ine cient asset formation motivated by tax arbitrage.... In PAGE 5: ... 2.1 The present tax system One causal chain underlying the empirical results of Table1 could be as follows: companies inherently sort themselves into low{investment and high{ investment categories, and then the tax code generates low tax rates for high investment companies. This chain of causality ignores the fact that rms are optimising.... ..."

### Table 1: Comparison of Object Location Systems. In this table, n is the number of nodes. For simplicity, we assume that the network diameter is polynomial in n, and that assume the number of objects is O(n). Both stretch and hops refer to an object search. Space assumes that the object IDs occupy a constant number of bytes. Insert cost shows the number of hops or messages needed for node insertion; a - means the system does not provide an algorithm. In RRVV, the number of changes needed is polylogarithmic, but they do not give an algorithm to make the changes. In most cases, the time for insertion is given with high probability. In some cases, various messages can be sent in parallel; we did not allow for this optimization in stating the bounds in this table.

"... In PAGE 2: ...4 Neither of these techniques are guaranteed to find objects. Table1 summarizes related work alongside our contributions. Systems with no entry in the Stretch, Metric column do not con- sider stretch at all; those with special assume the metric space has a certain low-expansion property described in Section 3.... In PAGE 2: ...sed for general metric spaces (i.e., spaces that do not meet the conditions assumed by PRR) to get results similar to those of Awerbuch and Peleg [1]. Table1 gives a summary of some of the previous results along with ours. Note that our result for general metrics can be improved using results of Thorup and Zwick [32] to use only O(n log n) space.... In PAGE 3: ... We also prove that an alternate scheme by Plaxton, Rajaraman, and Richa (called PRR v.0 in Table1 ) gives a low stretch solution for general metric spaces. This follows from arguments similar to those used by Bourgain [4] for metric embeddings.... ..."

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