2008 49th Annual IEEE Symposium on Foundations of Computer Science最新文献

{"title":"Truthful Approximation Schemes for Single-Parameter Agents","authors":"Peerapong Dhangwatnotai, Shahar Dobzinski, S. Dughmi, T. Roughgarden","doi":"10.1137/080744992","DOIUrl":"https://doi.org/10.1137/080744992","url":null,"abstract":"We present the first monotone randomized polynomial-time approximation scheme (PTAS) for minimizing the makespan of parallel related machines (Q||Cmax), the paradigmatic problem in single-parameter algorithmic mechanism design. This result immediately gives a polynomial-time, truthful (in expectation) mechanism whose approximation guarantee attains the best-possible one for all polynomial-time algorithms (assuming P not equal to NP). Our algorithmic techniques are flexible and also yield, among other results, a monotone deterministic quasi-PTAS for Q||Cmax and a monotone randomized PTAS for max-min scheduling on related machines.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126864688","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}

{"title":"On Basing Lower-Bounds for Learning on Worst-Case Assumptions","authors":"B. Applebaum, B. Barak, David Xiao","doi":"10.1109/FOCS.2008.35","DOIUrl":"https://doi.org/10.1109/FOCS.2008.35","url":null,"abstract":"We consider the question of whether P ne NP implies that there exists some concept class that is efficientlyrepresentable but is still hard to learn in the PAC model of Valiant (CACM '84), where the learner is allowed to output any efficient hypothesis approximating the concept, including an \"improper\" hypothesis that is not itself in the concept class. We show that unless the polynomial hierarchy collapses, such a statement cannot be proven via a large class of reductions including Karp reductions, truth-table reductions, and a restricted form of non-adaptive Turing reductions. Also, a proof that uses a Turing reduction of constant levels of adaptivity would imply an important consequence in cryptography as it yields a transformation from any average-case hard problem in NP to a one-way function. Our results hold even in the stronger model of agnostic learning. These results are obtained by showing that lower bounds for improper learning are intimately related to the complexity of zero-knowledge arguments and to the existence of weak cryptographic primitives. In particular, we prove that if alanguage L reduces to the task of improper learning of circuits, then, depending on the type of the reduction in use, either (1) L has a statistical zero-knowledge argument system, or (2) the worst-case hardness of L implies the existence of a weak variant of one-way functions defined by Ostrovsky-Wigderson (ISTCS '93). Interestingly, we observe that the converse implication also holds. Namely, if (1) or (2) hold then the intractability of L implies that improper learning is hard.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129247772","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}

{"title":"Approximation Algorithms for Single-minded Envy-free Profit-maximization Problems with Limited Supply","authors":"M. Cheung, Chaitanya Swamy","doi":"10.1109/FOCS.2008.15","DOIUrl":"https://doi.org/10.1109/FOCS.2008.15","url":null,"abstract":"We present the first polynomial-time approximation algorithms for single-minded envy-free profit-maximization problems (Guruswami et al., 2005) with limited supply. Our algorithms return a pricing scheme and a subset of customers that are designated the winners, which satisfy the envy-freeness constraint, whereas in our analyses, we compare the profit of our solution against the optimal value of the corresponding social-welfare-maximization (SWM) problem of finding a winner-set with maximum total value. Our algorithms take any LP-based alpha-approximation algorithm for the corresponding SWM problem as input and return a solution that achieves profit at least OPT/O (alpha ldr log umax), where OPT is the optimal value of the SWM problem, and umax is the maximum supply of an item. This immediately yields approximation guarantees of O(radicmlog umax) for the general single-minded envy-free problem; and O(log umax) for the tollbooth and highway problems (Guruswami et al., 2005), and the graph-vertex pricing problem (Balcan and Blum, 2006) (alpha = O(1) for all the corresponding SWM problems). Since OPT is an upper bound on the maximum profit achievable by any solution (i.e., irrespective of whether the solution satisfies the envy-freeness constraint), our results directly carry over to the non-envy-free versions of these problems too. Our result also thus (constructively) establishes an upper bound of O(alpha ldr log umax) on the ratio of (i) the optimum value of the profit-maximization problem and OPT; and (ii) the optimum profit achievable with and without the constraint of envy-freeness.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130568313","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}

{"title":"A Geometric Approach to Lower Bounds for Approximate Near-Neighbor Search and Partial Match","authors":"R. Panigrahy, Kunal Talwar, Udi Wieder","doi":"10.1109/FOCS.2008.68","DOIUrl":"https://doi.org/10.1109/FOCS.2008.68","url":null,"abstract":"This work investigates a geometric approach to proving cell probe lower bounds for data structure problems.We consider the {em approximate nearest neighbor search problem} on the Boolean hypercube $(bool^d,onenorm{cdot})$ with $d=Theta(log n)$. We show that any (randomized) data structure for the problem that answers $c$-approximate nearest neighbor search queries using $t$ probes must use space at least $n^{1+Omega(1/ct)}$. In particular, our bound implies that any data structure that uses space $tilde{O}(n)$ with polylogarithmic word size, and with constant probability gives a constant approximation to nearest neighbor search queries must be probed $Omega(log n/ loglog n)$ times. This improves on the lower bound of $Omega(loglog d/logloglog d)$ probes shown by Chakrabarti and Regev~cite{ChakrabartiR04} for any polynomial space data structure, and the $Omega(loglog d)$ lower bound in Patrascu and Thorup~cite{PatrascuT07} for linear space data structures.Our lower bound holds for the {em near neighbor problem}, where the algorithm knows in advance a good approximation to the distance to the nearest neighbor.Additionally, it is an {em average case} lower bound for the natural distribution for the problem. Our approach also gives the same bound for $(2-frac{1}{c})$-approximation to the farthest neighbor problem.For the case of non-adaptive algorithms we can improve the bound slightly and show a $Omega(log n)$ lower bound on the time complexity of data structures with $O(n)$ space and logarithmic word size.We also show similar lower bounds for the partial match problem: any randomized $t$-probe data structure that solves the partial match problem on ${0,1,star}^d$ for $d=Theta(log n)$ must use space $n^{1+Omega(1/t)}$. This implies an $Omega(log n/loglog n)$ lower bound for time complexity of near linear space data structures, slightly improving the $Omega(log n /(log log n)^2)$ lower bound from~cite{PatrascuT06a},cite{JayramKKR03} for this range of $d$. Recently and independently Patrascu achieved similar bounds cite{patrascu08}. Our results also generalize to approximate partial match, improving on the bounds of cite{BarkolR02,PatrascuT06a}.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127621384","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}

{"title":"Degree Bounded Network Design with Metric Costs","authors":"Yuk Hei Chan, W. Fung, L. Lau, Chun Kong Yung","doi":"10.1137/090746495","DOIUrl":"https://doi.org/10.1137/090746495","url":null,"abstract":"Given a complete undirected graph, a cost function on edges and a degree bound B, the degree bounded network design problem is to find a minimum cost simple subgraph with maximum degree B satisfying given connectivity requirements. Even for simple connectivity requirement such as finding a spanning tree, computing a feasible solution for the degree bounded network design problem is already NP-hard, and thus there is no polynomial factor approximation algorithm for this problem. In this paper, we show that when the cost function satisfies triangle inequalities, there are constant factor approximation algorithms for various degree bounded network design problems.Global edge-connectivity: There is a (2+1/k)-approximation algorithm for the minimum bounded degree k-edge-connected subgraph problem. Local edge-connectivity: There is a 6-approximation algorithm for the minimum bounded degree Steiner network problem. Global vertex-connectivity: there is a (2+(k-1)/n+1/k)-approximation algorithm for the minimum bounded degree k-vertex-connected subgraph problem. Spanning tree: there is an (1+1/(d-1))-approximation algorithm for the minimum bounded degree spanning tree problem. These approximation algorithms return solutions with smallest possible maximum degree, and the cost guarantee is obtained by comparing to the optimal cost when there are no degree constraints. This demonstrates that degree constraints can be incorporated into network design problems with metric costs.Our algorithms can be seen as a generalization of Christofides' algorithm for metric TSP. The main technical tool is a simplicity-preserving edge splitting-off operation, which is used to \"short-cut\" vertices with high degree while maintaining connectivity requirements and preserving simplicity of the solutions.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126375847","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}

{"title":"A Simpler Linear Time Algorithm for Embedding Graphs into an Arbitrary Surface and the Genus of Graphs of Bounded Tree-Width","authors":"K. Kawarabayashi, B. Mohar, B. Reed","doi":"10.1109/FOCS.2008.53","DOIUrl":"https://doi.org/10.1109/FOCS.2008.53","url":null,"abstract":"For every fixed surface S, orientable or non-orientable, and a given graph G, Mohar (STOC'96 and Siam J. Discrete Math. (1999)) described a linear time algorithm which yields either an embedding of G in S or a minor of G which is not embeddable in S and is minimal with this property. That algorithm, however, needs a lot of lemmas which spanned six additional papers. In this paper, we give a new linear time algorithm for the same problem. The advantages of our algorithm are the following: 1. The proof is considerably simpler: it needs only about 10 pages, and some results (with rather accessible proofs) from graph minors theory, while Mohar's original algorithm and its proof occupy more than 100 pages in total. 2. The hidden constant (depending on the genus g of the surface S) is much smaller. It is singly exponential in g, while it is doubly exponential in Mohar's algorithm. As a spinoff of our main result, we give another linear time algorithm, which is of independent interest. This algorithm computes the genus and constructs minimum genus embeddings of graphs of bounded tree-width. This resolves a conjecture by Neil Robertson and solves one of the most annoying long standing open question about complexity of algorithms on graphs of bounded tree-width.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134534996","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}

{"title":"Fast Modular Composition in any Characteristic","authors":"K. Kedlaya, C. Umans","doi":"10.1109/FOCS.2008.13","DOIUrl":"https://doi.org/10.1109/FOCS.2008.13","url":null,"abstract":"We give an algorithm for modular composition of degree n univariate polynomials over a finite field F_q requiring n ¹ ⁺ ^o(1) log¹ ⁺ ^o(1) q bit operations; this had earlier been achieved in characteristic n^o(1) by Umans (2008). As an application, we obtain a randomized algorithm for factoring degree n polynomials over F_q requiring (n^1.5 ⁺ ^o(1) + n ¹ ⁺ ^o(1) log q) log¹ ⁺ ^o(1) q bit operations, improving upon the methods of von zur Gathen & Shoup (1992) and Kaltofen & Shoup (1998). Our results also imply algorithms for irreducibility testing and computing minimal polynomials whose running times are best-possible, up to lower order terms.As in Umans (2008), we reduce modular composition to certain instances of multipoint evaluation of multivariate polynomials. We then give an algorithm that solves this problem optimally (up to lower order terms), in arbitrary characteristic. The main idea is to lift to characteristic 0, apply a small number of rounds of multimodular reduction, and finish with a small number of multidimensional FFTs. The final evaluations are then reconstructed using the Chinese Remainder Theorem. As a bonus, we obtain a very efficient data structure supporting polynomial evaluation queries, which is of independent interest. Our algorithm uses techniques which are commonly employed in practice, so it may be competitive for real problem sizes. This contrasts with previous asymptotically fast methods relying on fast matrix multiplication.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134322459","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}

{"title":"Constant-Time Approximation Algorithms via Local Improvements","authors":"H. N. Nguyen, Krzysztof Onak","doi":"10.1109/FOCS.2008.81","DOIUrl":"https://doi.org/10.1109/FOCS.2008.81","url":null,"abstract":"We present a technique for transforming classical approximation algorithms into constant-time algorithms that approximate the size of the optimal solution. Our technique is applicable to a certain subclass of algorithms that compute a solution in a constant number of phases. The technique is based on greedily considering local improvements in random order.The problems amenable to our technique include vertex cover, maximum matching, maximum weight matching, set cover, and minimum dominating set. For example, for maximum matching, we give the first constant-time algorithm that for the class of graphs of degree bounded by d, computes the maximum matching size to within epsivn, for any epsivn > 0, where n is the number of nodes in the graph. The running time of the algorithm is independent of n, and only depends on d and epsiv.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131772028","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}

{"title":"(Acyclic) Job Shops are Hard to Approximate","authors":"M. Mastrolilli, O. Svensson","doi":"10.1109/FOCS.2008.36","DOIUrl":"https://doi.org/10.1109/FOCS.2008.36","url":null,"abstract":"For every euro > 0, we show that the (acyclic) job shop problem cannot be approximated within ratio O(log1+euro lb), unless NP has quasi-polynomial Las-Vegas algorithms, and where lb denotes a trivial lower bound on the optimal value. This almost matches the best known results for acyclic job shops, since an O(log1+euro lb)-approximate solution can be obtained in polynomial time for every euro > 0. Recently, a PTAS was given for the job shop problem, where the number of machines and the number of operations per job are assumed to be constant. Under P ne NP, and when the number mu of operations per job is a constant, we provide an inapproximability result whose value grows with mu to infinity. Moreover, we show that the problem with two machines and the preemptive variant with three machines have no PTAS, unless NP has quasi-polynomial algorithms. These results show that the restrictions on the number of machines and operations per job are necessary to obtain a PTAS.In summary, the presented results close many gaps in our understanding of the hardness of the job shop problem and resolve (negatively) several open problems in the literature.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123559308","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}

{"title":"Matrix Sparsification for Rank and Determinant Computations via Nested Dissection","authors":"R. Yuster","doi":"10.1109/FOCS.2008.14","DOIUrl":"https://doi.org/10.1109/FOCS.2008.14","url":null,"abstract":"The nested dissection method developed by Lipton, Rose, and Tarjan is a seminal method for quickly performing Gaussian elimination of symmetric real positive definite matrices whose support structure satisfies good separation properties (e.g. planar). One can use the resulting LU factorization to deduce various parameters of the matrix. The main results of this paper show that we can remove the three restrictions of being \"symmetric\", being \"real\", and being \"positive definite\" and still be able to compute the rank and, when relevant, also the absolute determinant, while keeping the running time of nested dissection. Our results are based, in part, on an algorithm that, given an arbitrary square matrix A of order n having m non-zero entries, creates another square matrix B of order n + 2t = O(m) with the property that each row and each column of B contains at most three nonzero entries, and, furthermore, rank(B) = rank (A) + 2t and det(B) = det(A). The running time of this algorithm is only O(m), which is optimal.","PeriodicalId":217236,"journal":{"name":"2008 49th Annual IEEE Symposium on Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128289815","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}