D. Angluin and L. Valiant. Fast probabilistic algorithms for hamiltonian circuits and matchings. J. Comput. Syst. Sci., 18:155--193, 1979. Home/Search Document Not in Database Summary Related Articles Check |
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On The Probable Performance Of Heuristics - For Bandwidth Minimization (Correct)
....1 and V 2 . As we shall see, these cases differ from the rest and will be handled in Lemma 3.5. First however, we need a proposition concerning the binomial distribution, B(n; p) By definition if x 2 B(n; p) then P(x = k) n Gammak . The following proposition is from Angluin and Valiant [1]. Proposition 3.1: If x 2 B(n; p) then for any ffl, 0 ffl 1; P(x (1 Gamma ffl)np) e and P(x (1 ffl)np) e . Lemma 3.5: Let ffl 0; 0 p 1 be fixed, c = Gamma(1 ffl) ln(1 Gamma p ) ff = c ln n n. For almost all G 2 Psi n ( p) 1 Gamma ffl)p jV 1 j ....
Angluin, D., L. G. Valiant. "Fast Probabilistic Algorithms for Hamiltonian Circuits and Matchings". In Journal of Computer and System Sciences 18 , 155-193, 1979.
Randomized Selection in n + C + o(n) Comparisons - Gerbessiotis, Siniolakis (Correct)
....of x in this expression is the following one. # #1 1 i=0 # # i=2c#s . The sum in the term above gives the probability of having at least 2c#s t 2 successes in B 1 independent Bernoulli trials with probability of success q. Cherno# s upper bound [1] on the probability of having at least (1 #) B 1)q successes in such an experiment gives an upper bound of e (# (B 1)q) 3 . We set 2c#s t 2 = 1 #) B 1)q in this bound and get e (2c#s t 2 (B 1)q) We choose f(N) so that f(N) N t) 2 #s) A lower bound for 2c#s (B 1)q and an ....
D. Angluin and L. G. Valiant. Fast probabilistic algorithms for hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18:155-193, 1979.
Space-Efficient Routing Tables For Almost All - Networks And The (Correct)
....e 2k 3(n 1) 2.2) possibilities. The last inequality follows from a general estimate of the tail probability of the binomial distribution with s n the number of successful outcomes in n experiments with probability of success p = Namely, by Cherno# s bounds, in the form used in [1, 9], Pr( s n pn k) 2e k 3pn . 2.3) To describe G, it then su#ces to modify the old code of G by prefixing it with (i) a description of this discussion in O(1) bits; ii) the identity of node i in 1)# bits; iii) the value of k in 1)# bits, possibly adding nonsignificant ....
L.G. Valiant and D. Angluin, Fast probabilistic algorithms for Hamiltonian circuits and matchings, J. Comput. System Sci., 18 (1979), pp. 155--193.
Noise Tolerant Algorithms for Learning and Searching - Aslam (1995) (3 citations) (Correct)
....be the probability of at least n successes in m Bernoulli trials, where each trial has probability of success p. Similarly, let LE(p, m, n) be the probability of at most n successes in m Bernoulli trials, where each trial has probability of success p. Chernoffs bounds may then be stated as follows [3]: GE(p, m, mp(1 ( e mpa2 3 LE(p,m, mp(1 ( e mpa2 2 Furthermore, we often make use of the following properties of GE and LE: p p LE(p,m,n) LE(p ,m,n) p p GE(p,m,n) GE(p ,m,n) 4.2) 4.3) We may now prove following theorem. from query space Q with worst case relative ....
Dana Angluin and Leslie G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18(2):155-193, April 1979.
Improved Sampling with Applications to Dynamic Graph Algorithms. - Henzinger, Thorup (1996) (5 citations) (Correct)
.... Gamma 1= 4r) 4r ln ln s Gamma4r ln ln s= 4r) 1= ln s: Case 2: jRj=jSj 1= 4r) The algorithm did return an element in Step A.6, so jR 2 j 4 ln s. However, the expected value of jR 2 j is at most 2 ln s. Note that p = P r(jR 2 j (1 ffi ) with ffi = 1: Using a Chernoff bound from [2,9], P r(jR 2 j (1 ffi ) e Gamma2 ln s=3 Gamma2(e ln ln s) 3 1= ln s: Above, it was used that x= ln x e for any real x 0. We are now ready to show that Algorithm B satisfies the conditions of Lemma 1. i) First we find the expected number of samples if the algorithm ....
....we are returning in Step B.2.3. Then jR i j is at least x = n i . However, the expected value of jR i j is at most n i (1 Gamma n i Gamma1 =2:1) n i (1 Gamma 1= 2:1 lnn i ) Note that p i P r(jR i Gamma1 j (1 ffi ) with ffi = x Gamma ) Using the Chernoff bound (according to [2,9]) P r(jR i Gamma1 j (1 ffi ) e Gamma(x Gamma) 3) For n i (1 Gamma 1= 2:1 lnn i ) this function is maximized for = n i (1 Gamma 1= 2:1 lnn i ) Thus, Gamma(n i = 2:1 ln n i ) 3n i (1 Gamma 1= 2:1 lnn i ) Gamman i 13(ln n i ) 2 ) n For the last ....
D. Angluin, L. G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. J. Comput. System Sci. 18 (2), 1979, 155--193.
The efficiency of resolution and Davis-Putnam procedures - Beame, Karp, Pitassi (1999) (8 citations) (Correct)
.... are monotone (or anti monotone) with respect to sets of clauses, the almost certain properties under both distributions are the same up to a change from m to m o(m) This is just a natural extension of the similar (and more precise) equivalences for the random graph model as shown for example in [AV79]. We generally assume the distribution F m . We write F F to mean F is a random formula selected according to distribution F . We make frequent use of two well known tail bounds for the binomial distribution (see [ASE92] Appendix A) Proposition 6: If Y is a random variable distributed ....
D. Angluin and L. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18:155--193, 1979.
Selection on the Bulk-Synchronous Parallel Model with.. - Gerbessiotis, Siniolakis (1996) (12 citations) (Correct)
.... The random distribution of items to processors (line 8) requires at most max fL; grg time with probability 1 Gamma O(n ) for any constant ae 0, where r = d(1 ) n=p)e, and = O( 1= n ) This claim can be derived by way of Chernoff bounds on the right tail of the binomial distribution [1]. For the remainder of this proof, we therefore assume that each processor has at most r = d(1 ) n=p)e items from any node in Q. The median selection process (line 10) takes at most T sel (2pr; n; p) time. We note that we use the expression 2pr to compensate for the uneven distribution of items ....
D. Angluin and L. G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18:155-193, 1979.
Concurrent Heaps on the BSP Model - Gerbessiotis, Siniolakis (1996) (Correct)
....q(1 Gamma x) The coefficient of x in this expression is the following one. The sum in the term above gives the probability of having at least 2cs Gamma t=2 successes in B 1 independent Bernoulli trials with probability of success q. Chernoff s upper bound [1] on the probability of having at least (1 fi) B 1)q successes in such an experiment gives an upper bound of e Gamma(fi (B 1)q) 3 . We set 2cs Gamma t=2 = 1 fi) B 1)q in this bound and get e . We choose the function f(N) so that f(N) N t) 2 s) A lower bound for 2cs Gamma ....
....1: In step 1, at most max fL; d2=peg time is spent on each processor for random processor identifier generation. We distinguish four cases in the analysis of step 2. Case 1: If d2=pe 3ae log n and since processor identifiers are selected uniformly at random, then the the probability bound in [1], Prob[S n;P (1 ) nP ] e , 0 1, where S n;P is the number of successes in n independent Bernoulli trials with individual probability of success P , for n = 2 Gamma 1, P = 1=p and = 1 Gamma o(1) shows that with probability 1 Gamma O(n ) for any ae 1, no processor gets ....
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D. Angluin and L. G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18:155-193, 1979.
Noise Tolerant Algortihms for Learning and Searching - Aslam (1995) (Correct)
....the probability of at least n successes in m Bernoulli trials, where each trial has probability of success p. Similarly, let LE(p; m; n) be the probability of at most n successes in m Bernoulli trials, where each trial has probability of success p. Chernoff s bounds may then be stated as follows [3]: GE(p; m;mp(1 ff) e LE(p; m; mp(1 Gamma ff) e Furthermore, we often make use of the following properties of GE and LE: LE(p; m; n) LE(p = GE(p; m; n) GE(p We may now prove following theorem. Theorem 10 If F is learnable by a statistical query algorithm which makes ....
Dana Angluin and Leslie G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18(2):155--193, April 1979.
Approximation Algorithms Via Randomized Rounding: A Survey - Srinivasan (Correct)
.... (7) For ffi 2 [0; 1] Hoeffding s approach also gives Pr[X (1 Gamma ffi) Pr[n Gamma X n Gamma (1 Gamma ffi) F (n; Gammaffi ) 1 Gamma ffi (n Gamma(1 Gammaffi) n Gamma(1 Gammaffi) 1 Gamma ffi) 1 Gammaffi) 8) The following related results are useful (see, e.g. [33, 5, 4, 56]) If ffi 0, Pr[X (1 ffi) Q i2[n] E[ 1 ffi) X i ] 1 ffi) 1 ffi) G( ffi) e ffi (1 ffi) 1 ffi) 9) If ffi 2 [0; 1] Pr[X (1 Gamma ffi) Q i2[n] E[ 1 Gamma ffi) X i ] 1 Gamma ffi) 1 Gammaffi) H( ffi) e Gammaffi 2 =2 : 10) It can ....
D. Angluin and L.G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18:155--193, 1979.
On the Learnability of Boolean Formulae - Michael Kearns Harvard (1987) (56 citations) Self-citation (Valiant) (Correct)
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D. Angluin and L.G. Valiant. Fast Probabilistic Algorithms for Hamiltonian Circuits and Matchings. JCSS, 18(2):155-193, 1979.
A General Lower Bound on the Number - Of Examples Needed Self-citation (Valiant) (Correct)
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Angluin, D., L.G. Valiant, "Fast probabilistic algorithms for Hamiltonian circuits and matchings", Journal of Computer and Systems Sciences, 18, 1979, pp. 155-193.
Cryptographic Limitations on Learning - Boolean Formulae And Self-citation (Valiant) (Correct)
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D. Angluin, L.G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and Systems Sciences, 18, 1979, pp. 155-193.
Online Performance-Improvement - Prasad Chalasani August (Correct)
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D. Angluin and L. Valiant. Fast probabilistic algorithms for hamiltonian circuits and matchings. J. Comput. Syst. Sci., 18:155--193, 1979.
Optimal Parallel Construction of Hamiltonian Cycles and.. - MacKenzie, Stout (1993) (1 citation) (Correct)
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D. Angluin and L. G. Valiant. Fast probabilistic algorithms for hamiltonian circuits and matchings. J. Comput. System Sci., 18:155--193, 1979.
Concentration Bounds for Unigrams Language Model - Drukh, Mansour (2004) (Correct)
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D. Angluin and L. G. Valiant. Fast Probabilistic Algorithms for Hamiltonian Circuits and matchings, In Journal of Computer and System Sciences, 18:155-193, 1979.
Learning in the Presence of Malicious Errors - Michael Kearns Att (1993) (81 citations) (Correct)
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D. Angluin, L.G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and Systems Sciences, 18, 1979, pp. 155-193. 32
Efficient Distribution-free Learning of Probabilistic Concepts - Kearns, Schapire (1993) (108 citations) (Correct)
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Dana Angluin and Leslie G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18(2):155--193, April 1979.
The Efficiency of Resolution and Davis-Putnam Procedures - Beame, Karp, Pitassi, Saks (1999) (8 citations) (Correct)
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D. Angluin and L. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18:155-193, 1979.
Deterministic Design for Neural Network Learning: - An Approach Based (Correct)
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D. Angluin and L. Valiant, "Fast probabilistic algorithms for hamiltonian circuits and matchings," Journal of Computer and System Science, vol. 18, pp. 155--193, 1979.
A Distributed Algorithm To Find Hamiltonian Cycles In.. - Levy, Louchard, Petit (2000) (Correct)
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D. Angluin and L. G. Valiant. Fast probabilistic algorithms for hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18:155-193, 1979.
Unknown - (Correct)
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D. Angluin and L. G. Valiant. Fast probabilistic algorithms for hamiltonian circuits and matchings. J. Computer and System Sciences, 18:155--193, 1979.
The Resolution Complexity of Random Graph k-Colorability - Beame, Culberson, al. (2003) (Correct)
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D. Angluin and L. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18:155--193, 1979.
Almost All - Graphs Are Easy (Correct)
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Angluin, D., L. G. Valiant. "Fast Probabilistic Algorithms for Hamiltonian Circuits and Matchings." In Journal of Computer and System Sciences 18 , 155--193, 1979.
A probabilistic analysis of the Floyd-Rivest expected.. - Gerbessiotis, Siniolakis (2002) (Correct)
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D. Angluin and L. G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Journal of Computer and System Sciences, 18:155-193, 1979.
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