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## DOI 10.1287/moor.xxxx.xxxx c○20xx INFORMS Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders

### Citations

844 | The space complexity of approximating the frequency moments
- ALON, MATIAS, et al.
- 1996
(Show Context)
Citation Context ...ill see that A ≥ Σivi(S) 3 with high probability. We make use of the following corollary from Chebyshev’s inequality: Lemma 3.2 Let X be the sum of independent random variables, each of which lies in =-=[0, 1]-=-, and let µ = E[X]. Then, for any α > 0, Pr[|X − µ| ≥ α] ≤ µ α 2 . We can now upper bound the probability that event B occurs. ∗ OP T Pr[B] = Pr[A < ] ≤ Pr[|A − OP T 3 ∗ ∗ 2OP T 9 3 | ≥ ] ≤ ≤ 3 4OP T ... |

774 | A threshold of ln n for approximating set cover
- Feige
- 1998
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Citation Context ...om MAX-k-COVER. MAX-k-Cover is defined as follows: Given m items, and a collection of subsets of these items, the objective is to maximize the number of items which can be covered by k subsets. Feige =-=[8]-=- proved that it is NP-hard to approximate this problem within a better factor than e e−1 . This problem can be converted into a combinatorial auction with XOS valuations: given an instance of MAX-k-CO... |

458 | Combinatorial auctions. - Cramton, Shoham, et al. - 2006 |

216 | Computationally feasible VCG mechanisms.
- Nisan, Ronen
- 2007
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Citation Context ... an approximation algorithm and using the VCG payment scheme (paying each bidder the sum of the utilities of the rest of the bidders) does not result in a truthful mechanism. In fact, Nisan and Ronen =-=[18]-=- show that an approximation algorithm becomes truthful using the VCG payment scheme if and only if the underlying algorithm, is essentially maximal in range. An algorithm is maximal in range if it lim... |

202 | Combinatorial auctions with decreasing marginal utilities.
- Lehmann, Lehmann, et al.
- 2005
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Citation Context ...inatorial auctions is the one in which the valuations are known to be complement-free, i.e., all input valuations are known to be subadditive: v(S ∪ T ) ≤ v(S) + v(T ) for all S, T 1 . Lehmann et al. =-=[12]-=- exhibit a strict hierarchy of subclasses within this class of valuations: OXS ⊂ GS ⊂ SM ⊂ XOS ⊂ CF . The CF and SM classes are easy to define: CF is the class of subadditive (complement-free) valuati... |

134 | The Communication requirements of efficient allocations and supporting lindahl prices.
- Nisan, Segal
- 2001
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Citation Context ... polynomial time algorithm exists if the input valuations are given in the OXS language; a polynomial time algorithm, based on linear programming, exists for the class GS, as shown by Nisan and Segal =-=[19]-=-. For the SM class no polynomial time algorithm exists – an NP-hardness result for a simple submodular bidding language is shown in a paper by Lehmann et al. [12], and an exponential communication low... |

123 | Optimal approximation for the Submodular Welfare Problem in the value oracle model.
- Vondrak
- 2008
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Citation Context ...ed to an unconditional one by Mirrokni et al. [?].4 Dobzinski et al.: Approximations Algorithms for CA’s with CF Bidders Mathematics of Operations Research 00(0), pp. xxx–xxx, c○20xx INFORMS Vondrak =-=[21]-=- has shown that this lower bound is tight by exhibiting a matching upper bound that uses value queries only. In the demand queries model Feige and Vondrak [10] obtained an approximation ratio slightly... |

105 | Truthful randomized mechanisms for combinatorial auctions.
- Dobzinski, Nisan, et al.
- 2006
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Citation Context ...orithm has several advantages: it is combinatorial, fast, simple, and deterministic. Moreover, it serves as the main building block for constructions of truthful mechanisms for combinatorial auctions =-=[4, 6]-=-. 1.2 Lower Bounds. We prove lower bounds for approximation for both CF and XOS. The class CF does not have a natural bidding language and so the lower bound is for the oracle model. The lower bound f... |

77 | Liadan Ita O’Callaghan, and Yoav Shoham. Truth revelation in approximately efficient combinatorial auctions - Lehmann - 2002 |

59 | Approximation algorithms for allocation problems: Improving the factor of 1-1/e. In:
- Feige, Vondrak
- 2006
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Citation Context ...(0), pp. xxx–xxx, c○20xx INFORMS Vondrak [21] has shown that this lower bound is tight by exhibiting a matching upper bound that uses value queries only. In the demand queries model Feige and Vondrak =-=[10]-=- obtained an approximation ratio slightly better than e e−1 . They also show that approximating the welfare with demand oracle in this case is APX-hard. Another line of research which stemmed in this ... |

32 | The communication complexity of approximate set packing and covering.
- Nisan
- 2002
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Citation Context ...also possible to consider the “dual” class of substitute-free valuations (v(S ∪ T ) ≥ v(S) + v(T ), for disjoint S, T ⊆ M). However, it turns out that the lower bound for general valuations, by Nisan =-=[15]-=-, also applies to this class.Dobzinski et al.: Approximations Algorithms for CA’s with CF Bidders Mathematics of Operations Research 00(0), pp. xxx–xxx, c○20xx INFORMS 3 This algorithm is based on ca... |

28 |
Algorithms for Optimal Winner Determination in
- Sandholm
- 2002
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Citation Context ...ctor of O( √ m) in polynomial time, but not within a factor of m 1/2−ɛ , for any constant ɛ > 0. This is true even for the case of single-minded bidders, as shown by Lehmann et al. [13], and Sandholm =-=[20]-=-. The lower bound holds even for the general queries model, whereas the upper bound requires demand queries, but value queries do not suffice [7, 2]. An important special case of combinatorial auction... |

18 | On the computational power of iterative auctions I: Demand queries.
- Blumrosen, Nisan
- 2005
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Citation Context ... j∈S pj. This query is natural from an economic point of view as it corresponds to the revealed preferences of the bidders (i.e., what is directly observable from their behavior). Blumrosen and Nisan =-=[2]-=- and Dobzinski and Schapira [7] showed that demand queries are strictly stronger than value queries (in the sense that value queries can be simulated by a polynomial number of demand queries, but expo... |

8 | Optimal upper and lower approximation bounds for k-duplicates combinatorial auctions. Working paper, the Hebrew
- Dobzinski, Schapira
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Citation Context ...from an economic point of view as it corresponds to the revealed preferences of the bidders (i.e., what is directly observable from their behavior). Blumrosen and Nisan [2] and Dobzinski and Schapira =-=[7]-=- showed that demand queries are strictly stronger than value queries (in the sense that value queries can be simulated by a polynomial number of demand queries, but exponential number of value queries... |

6 |
Evangelos Markakis, and Aranyak Mehta, Inapproximability results for combinatorial auctions with submodular utility functions, Algorithmica 52
- Khot, Lipton
- 2008
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Citation Context ...ses demand queries. The communication lower bound we present implies that this upper bound is tight. We now discuss subsequent work related to submodular valuations. Khot, Lipton, Markakis, and Mehta =-=[11]-=- showed that no approximation better than e e−1 using value queries only is possible, unless P = NP . This lower bound was recently strengthened to an unconditional one by Mirrokni et al. [?].4 Dobzi... |

1 |
maximizing welfare when utility functions are subadditive
- On
- 2006
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Citation Context ...s only value queries, requires an exponential number of queries to achieve an approximation ratio better than m 1 2 −ɛ , for any constant ɛ > 0. 1.4 Subsequent Work. Subsequently to this paper, Feige =-=[9]-=- improved the upper bound for combinatorial auctions with complement-free valuations to 2. This upper bound uses demand queries. The communication lower bound we present implies that this upper bound ... |