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Causal sets: Discrete gravity
, 2003
"... These are some notes in lieu of the lectures I was scheduled to give, but had to cancel at the last moment. In some places, they are more complete, in others much less so, regrettably. I hope they at least give a feel for the subject and convey some of the excitement felt at the moment by those of u ..."
Abstract

Cited by 21 (0 self)
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These are some notes in lieu of the lectures I was scheduled to give, but had to cancel at the last moment. In some places, they are more complete, in others much less so, regrettably. I hope they at least give a feel for the subject and convey some of the excitement felt at the moment by those of us working on it. An extensive set of references and a glossary of terms can be found at the end of the notes. For a philosophically oriented discussion of some of the background to the causal set idea,
Searching in random partially ordered sets
, 2004
"... We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing e3ciently nearoptimal search strategies for typical partial orders under two classical models for random partial orders, the random graph model and the uniform mo ..."
Abstract

Cited by 12 (2 self)
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We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing e3ciently nearoptimal search strategies for typical partial orders under two classical models for random partial orders, the random graph model and the uniform model. We shall show that the problem of determining an optimal strategy is NPhard, but there are simple, fast algorithms able to produce nearoptimal search strategies for typical partial orders under the two models of random partial orders that we consider. We present a (1 + o(1))approximation algorithm for typical partial orders under the random graph model (constant p) and present a 6.34approximation algorithm for typical partial orders under the uniform model. Both algorithms run in polynomial time.
Causal sets: Discrete gravity,” grqc/0309009; T. Padmanabhan, “Dark Energy: Mystery of the Millennium,” astroph/0603114
 In
"... These are some notes in lieu of the lectures I was scheduled to give, but had to cancel at the last moment. In some places, they are more complete, in others much less so, regrettably. I hope they at least give a feel for the subject and convey some of the excitement felt at the moment by those of u ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
These are some notes in lieu of the lectures I was scheduled to give, but had to cancel at the last moment. In some places, they are more complete, in others much less so, regrettably. I hope they at least give a feel for the subject and convey some of the excitement felt at the moment by those of us working on it. An extensive set of references and a glossary of terms can be found at the end of the notes. For a philosophically oriented discussion of some of the background to the causal set idea,
SEE PROFILE
, 2003
"... We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing e3ciently nearoptimal search strategies for typical partial orders under two classical models for random partial orders, the random graph model and the uniform mo ..."
Abstract
 Add to MetaCart
We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing e3ciently nearoptimal search strategies for typical partial orders under two classical models for random partial orders, the random graph model and the uniform model. We shall show that the problem of determining an optimal strategy is NPhard, but there are simple, fast algorithms able to produce nearoptimal search strategies for typical partial orders under the two models of random partial orders that we consider. We present a (1 + o(1))approximation algorithm for typical partial orders under the random graph model (constant p) and present a 6.34approximation algorithm for typical partial orders under the uniform model. Both algorithms run in polynomial time.