48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)最新文献_第3页

Towards Sharp Inapproximability For Any 2-CSP 对任意2-CSP的尖锐不逼近性

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1137/070711670

Per Austrin

{"title":"Towards Sharp Inapproximability For Any 2-CSP","authors":"Per Austrin","doi":"10.1137/070711670","DOIUrl":"https://doi.org/10.1137/070711670","url":null,"abstract":"We continue the recent line of work on the connection between semidefinite programming-based approximation algorithms and the Unique Games Conjecture. Given any-boolean 2-CSP (or more generally, any nonnegative objective function on two boolean variables), we show how to reduce the search for a good inapproximability result to a certain numeric minimization problem. The key objects in our analysis are the vector triples arising when doing clause-by-clause analysis of algorithms based on semidefinite programming. Given a weighted set of such triples of a certain restricted type, which are \"hard\" to round in a certain sense, we obtain a Unique Games-based inapproximability matching this \"hardness\" of rounding the set of vector triples. Conversely, any instance together with an SDP solution can be viewed as a set of vector triples, and we show that we can always find an assignment to the instance which is at least as good as the \"hardness\" of rounding the corresponding set of vector triples. We conjecture that the restricted type required for the hardness result is in fact no restriction, which would imply that these upper and lower bounds match exactly. This conjecture is supported by all existing results for specific 2-CSPs. As an application, we show that Max 2-AND is hard to approximate within 0.87435. This improves upon the best previous hardness of alphaGW + epsi ap 0.87856, and comes very close to matching the approximation ratio of the best algorithm known, 0.87401. It also establishes that balanced instances of Max 2-AND, i.e., instances in which each variable occurs positively and negatively equally often, are not the hardest to approximate, as these can be approximated within a factor alphaGW.","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117060741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 75

Hardness Amplification for Errorless Heuristics 无误差启发式的硬度放大

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.25

Andrej Bogdanov, S. Safra

{"title":"Hardness Amplification for Errorless Heuristics","authors":"Andrej Bogdanov, S. Safra","doi":"10.1109/FOCS.2007.25","DOIUrl":"https://doi.org/10.1109/FOCS.2007.25","url":null,"abstract":"An errorless heuristic is an algorithm that on all inputs returns either the correct answer or the special symbol perp, which means \"I don't know,\" A central question in average-case complexity is whether every distributional decision problem in N P has an errorless heuristic scheme: This is an algorithm that, for every delta > 0, runs in time polynomial in the instance size and | / delta and answers perp only on a delta fraction of instances. We study the question from the standpoint of hardness amplification and show that If every problem in (NP,U) has errorless heuristic circuits that output the correct answer on n -2/9+omicron(1)-fraction of inputs, then (NP,U) has non-uniform errorless heuristic schemes. If every problem in (NP,U) has randomized errorless heuristic algorithms that output the correct answer on (log n)-1/10+omicron(1)-fraction of inputs, then (NP.W) has randomized errorless heuristic schemes. In both cases, the low-end amplification is achieved by analyzing a new sensitivity property of monotone boolean Junctions in NP. In the non-uniform setting we use a \" holographic Junction\" introduced by Benjamini, Schramm, and Wilson (STOC 2005). For the uniform setting we introduce a new Junction that can be viewed as an efficient version of Talagrand's \"random DNF\".","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128746957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 24

Approximation Algorithms for Partial-Information Based Stochastic Control with Markovian Rewards 基于部分信息的马尔可夫奖励随机控制的逼近算法

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.12

S. Guha, Kamesh Munagala

{"title":"Approximation Algorithms for Partial-Information Based Stochastic Control with Markovian Rewards","authors":"S. Guha, Kamesh Munagala","doi":"10.1109/FOCS.2007.12","DOIUrl":"https://doi.org/10.1109/FOCS.2007.12","url":null,"abstract":"We consider a variant of the classic multi-armed bandit problem (MAB), which we call feedback MAB, where the reward obtained by playing each of n independent arms varies according to an underlying on/off Markov process with known parameters. The evolution of the Markov chain happens irrespective of whether the arm is played, and furthermore, the exact state of the Markov chain is only revealed to the player when the arm is played and the reward observed. At most one arm (or in general, M arms) can be played any time step. The goal is to design a policy for playing the arms in order to maximize the infinite horizon time average expected reward. This problem is an instance of a partially observable Markov decision process (POMDP), and a special case of the notoriously intractable \"restless bandit\" problem. Unlike the stochastic MAB problem, the feedback MAB problem does not admit to greedy index-based optimal policies. Vie state of the system at any time step encodes the beliefs about the states of different arms, and the policy decisions change these beliefs - this aspect complicates the design and analysis of simple algorithms. We design a constant factor approximation to the feedback MAB problem by solving and rounding a natural LP relaxation to this problem. As far as we are aware, this is the first approximation algorithm for a POMDP problem.","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128146193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 59

Planning for Fast Connectivity Updates 规划快速连接更新

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.54

M. Patrascu, Mikkel Thorup

引用次数: 80

Can you beat treewidth? 你能打败树宽吗?

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.4086/toc.2010.v006a005

D. Marx

引用次数: 194

Strong Lower Bounds for Approximating Distribution Support Size and the Distinct Elements Problem 近似分布支撑尺寸的强下界及不同元问题

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.67

Sofya Raskhodnikova, D. Ron, Amir Shpilka, Adam D. Smith

引用次数: 136

Any AND-OR Formula of Size N can be Evaluated in time N^{1/2 + o(1)} on a Quantum Computer 在量子计算机上，任何大小为N的与或公式都可以在N^{1/2 + o(1)}时间内求值

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1137/080712167

A. Ambainis, Andrew M. Childs, B. Reichardt, R. Spalek, Shengyu Zhang

引用次数: 203

Non-Preemptive Min-Sum Scheduling with Resource Augmentation 具有资源扩充的非抢占最小和调度

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.46

N. Bansal, H. Chan, R. Khandekar, K. Pruhs, C. Stein, B. Schieber

引用次数: 32

Intrusion-Resilient Secret Sharing 入侵弹性秘密共享

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.63

Stefan Dziembowski, Krzysztof Pietrzak

{"title":"Intrusion-Resilient Secret Sharing","authors":"Stefan Dziembowski, Krzysztof Pietrzak","doi":"10.1109/FOCS.2007.63","DOIUrl":"https://doi.org/10.1109/FOCS.2007.63","url":null,"abstract":"We introduce a new primitive called intrusion-resilient secret sharing (IRSS), whose security proof exploits the fact that there exist functions which can be efficiently computed interactively using low communication complexity in k, but not in k-1 rounds. IRSS is a means of sharing a secret message amongst a set of players which comes with a very strong security guarantee. The shares in an IRSS are made artificially large so that it is hard to retrieve them completely, and the reconstruction procedure is interactive requiring the players to exchange k short messages. The adversaries considered can attack the scheme in rounds, where in each round the adversary chooses some player to corrupt and some function, and retrieves the output of that function applied to the share of the corrupted player. This model captures for example computers connected to a network which can occasionally he infected by malicious software like viruses, which can compute any function on the infected machine, but cannot sent out a huge amount of data. Using methods from the bounded-retrieval model, we construct an IRSS scheme which is secure against any computationally unbounded adversary as long as the total amount of information retrieved by the adversary is somewhat less than the length of the shares, and the adversary makes at most k-1 corruption rounds (as described above, where k rounds are necessary for reconstruction). We extend our basic scheme in several ways in order to allow the shares sent by the dealer to be short (the players then blow them up locally) and to handle even stronger adversaries who can learn some of the shares completely. As mentioned, there is an obvious connection between IRSS schemes and the fact that there exist functions with an exponential gap in their communication complexity for k and k-1 rounds. Our scheme implies such a separation which is in several aspects stronger than the previously known ones.","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127454331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 147

Balloon Popping With Applications to Ascending Auctions 气球爆裂与应用上升拍卖

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.15

Nicole Immorlica, Anna R. Karlin, Mohammad Mahdian, Kunal Talwar

引用次数: 10