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OR-parallel theorem proving with random competition
[chapter]
Logic Programming and Automated Reasoning
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With random competition we propose a method for parallelizing backtracking search. We can prove high efficiency of random competition on highly parallel architectures with thousands of processors. ...
OR-parallel search in general. ...
The basic idea of random competition is to use a set of independent parallel processors, each of them executing a different randomized search strategy for proving a theorem. ...
doi:10.1007/bfb0013064
dblp:conf/lpar/Ertel92
fatcat:fvf4x4q7q5hqno7v4cdjgsczr4
Randomized algorithms for on-line scheduling problems: how low can't you go?
2002
Operations Research Letters
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Theorem 4.4 Any randomized algorithm for the on-line makespan problem on identical parallel machines has a competitive ratio against an oblivious adversary greater or equal to 4 -2V2. ...
Theorem 4. 3 3 Any randomized algorithm for the on-line maximum delivery time problem on identical parallel machines has a competitive ratio against an oblivious adversary greater or equal to 1.265. ...
doi:10.1016/s0167-6377(01)00115-8
fatcat:7fdmz66ngjhsjccqmebpmjn4oq
A $$o(n)$$ -Competitive Deterministic Algorithm for Online Matching on a Line
[chapter]
2015
Lecture Notes in Computer Science
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Online matching on a line involves matching an online stream of items of various sizes to stored items of various sizes, with the objective of minimizing the average discrepancy in size between matched ...
The best previously known upper and lower bounds on the optimal deterministic competitive ratio are linear in the number of items, and constant, respectively. ...
We note that, in a manner similar to that presented in Section 4, it is possible to extend the Parallel Cows algorithm for k-LCWA to OML directly and obtain an O p log 2 (3+ )−1 / -competitive algorithm ...
doi:10.1007/978-3-319-18263-6_2
fatcat:chcry2oecfbdzkvnhossx65mam
Page 7794 of Mathematical Reviews Vol. , Issue 95m
[page]
1995
Mathematical Reviews
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The authors first prove two theorems, the pattern limit theorem and the collective limit theorem. ...
In a similar way we prove that the competitive ratio for the randomized case is k’ = In(m) (up to an additive 1). ...
Lower bounds for on-line scheduling with precedence constraints on identical machines
[chapter]
1998
Lecture Notes in Computer Science
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2=(m+1) on the competitive ratio of any randomized algorithm (with or without preemption). The lower bounds for the cases that preemption is allowed require arbitrarily long sequences. ...
1=m on the competitive ratio of any deterministic algorithm (with or without preemption) and a lower bound of 2 ? ...
We use the sequence from Theorem 2 with k = 1. ...
doi:10.1007/bfb0053966
fatcat:knvtij4r5zd7fei4r5xdgbpyqi
The matroid secretary problem for minor-closed classes and random matroids
[article]
2019
arXiv
pre-print
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We also note that for asymptotically almost all matroids, the matroid secretary algorithm that selects a random basis, ignoring weights, is (2+o(1))-competitive. ...
We prove that for every proper minor-closed class M of matroids representable over a prime field, there exists a constant-competitive matroid secretary algorithm for the matroids in M. ...
Finally, in Section 8, we prove our results on random matroids. ...
arXiv:1603.06822v5
fatcat:q3dfe33ctfdizdadd2qoyhruby
Matroid Secretary Problem in the Random Assignment Model
[article]
2010
arXiv
pre-print
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Our main result is the first constant competitive algorithm for the matroid secretary problem in the random assignment model. This solves an open question of Babaioff et al. ...
When an element is revealed, the algorithm learns its weight and decides whether or not to select it under the restriction that the selected elements form an independent set in the matroid. ...
To prove Theorem 4.3, we compare the weight of the set ALG returned by Algorithm 2 with the optimum of the partition matroid P defined above. ...
arXiv:1007.2152v1
fatcat:eccprmcek5dcfjmfawhlamxuju
Online Scheduling of Task Graphs on Heterogeneous Platforms
2019
IEEE Transactions on Parallel and Distributed Systems
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We prove that no online algorithm can have a competitive ratio smaller than m/k. ...
We also study how adding flexibility on task processing, such as task migration or spoliation, or increasing the knowledge of the scheduler by providing it with information on the task graph, influences ...
Theorem 3. The lower bounds proved in Theorems 1 and 2 on the competitive ratio of deterministic algorithms not using migration hold for randomized algorithms, divided by a factor 2. Proof. ...
doi:10.1109/tpds.2019.2942909
fatcat:glyainqq6rf4vn37zqhkxwlxca
Online Routing in Triangulations
2004
SIAM journal on computing (Print)
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Our results include (1) two deterministic memoryless routing algorithms, one that works for all Delaunay triangulations and the other that works for all regular triangulations; (2) a randomized memoryless ...
memory algorithm that works for all convex subdivisions; (4) an O(1) memory algorithm that approximates the shortest path in Delaunay triangulations; and (5) theoretical and experimental results on the competitiveness ...
We refer to the combination of the Voronoi routing algorithm with this parallel search algorithm as the parallel Voronoi routing algorithm. Theorem 3.6. ...
doi:10.1137/s0097539700369387
fatcat:zqgjya3ho5fwth2rtfnob2nsfi
Matroid Secretary Problem in the Random Assignment Model
[chapter]
2011
Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms
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As the main result of this article, we devise the first constant competitive algorithm for the model in which both the order and the weight assignment are selected uniformly at random, achieving a competitive ...
for the stronger random-assignment adversarial-order model. ...
Every color is successful with probability at least p(1−p)q(1−q). Before proving this proposition, let's use it to prove the main theorem of this section. Theorem 3.6. ...
doi:10.1137/1.9781611973082.97
dblp:conf/soda/Soto11
fatcat:wvy3s4seqfb5zop52ayutdncm4
Matroid Secretary Problem in the Random-Assignment Model
2013
SIAM journal on computing (Print)
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As the main result of this article, we devise the first constant competitive algorithm for the model in which both the order and the weight assignment are selected uniformly at random, achieving a competitive ...
for the stronger random-assignment adversarial-order model. ...
Every color is successful with probability at least p(1−p)q(1−q). Before proving this proposition, let's use it to prove the main theorem of this section. Theorem 3.6. ...
doi:10.1137/110852061
fatcat:y2hd6hftr5enfccc2uy55g2yiy
On-line scheduling to minimize max flow time: an optimal preemptive algorithm
2005
Operations Research Letters
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Moreover, when the algorithm must schedule jobs one by one in the order they are released, we prove that there is no randomized on-line algorithm with a better competitive ratio. ...
We derive an on-line algorithm with competitive ratio 2 − 1/m. ...
We prove the theorem by giving a lower bound of 2 − 1/m − ε on the competitive ratio, for any fixed ε > 0. ...
doi:10.1016/j.orl.2004.10.006
fatcat:tlxij7utune3ljeigezxziueiu
Online Routing in Triangulations
[chapter]
1999
Lecture Notes in Computer Science
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Our results include (1) two deterministic memoryless routing algorithms, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a randomized memoryless ...
memory algorithm that works for all convex subdivisions, (4) an O(1) memory algorithm that approximates the shortest path in Delaunay triangulations, and (5) theoretical and experimental results on the competitiveness ...
They also describes an O(1) memory routing algorithm that is not defeated by any connected planar graph, thus proving a stronger result than Theorem 2.7. ...
doi:10.1007/3-540-46632-0_12
fatcat:sfmqahv6lrbcxk5af7kqca3t7y
Witness indistinguishable and witness hiding protocols
1990
Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90
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Proof (sketch): Consider polynomially many protocols carried out concurrently (sequentially, in parallel, or with interleaved steps). ...
The probability space is that of the random choices of c~ together with P's random coin tosses. <~ Theorem 5.2: Any NIZK proof system is also a NIWI proof system. ...
doi:10.1145/100216.100272
dblp:conf/stoc/FeigeS90
fatcat:zsg4g67tzrbjpfekhg2lt6n2ui
LP-Based Online Scheduling: From Single to Parallel Machines
[chapter]
2005
Lecture Notes in Computer Science
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Additionally, we show how to combine randomization techniques with the linear programming approach to obtain randomized algorithms for both versions of the problem with competitive ratio strictly smaller ...
Specifically, we look at deterministic and randomized algorithms for the problem of scheduling jobs with release dates on identical parallel machines, to minimize the sum of weighted completion times: ...
We specially thank another anonymous referee for pointing out an error in a preliminary version of Theorem 5.3. ...
doi:10.1007/11496915_15
fatcat:x44sqaggxje4vg2xu6futo6koi
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