Showing papers by "Aravind Srinivasan published in 1999"

Improved Approximation Guarantees for Packing and Covering Integer Programs

Abstract: Several important NP-hard combinatorial optimization problems can be posed as packing/covering integer programs; the randomized rounding technique of Raghavan and Thompson is a powerful tool with which to approximate them well. We present one elementary unifying property of all these integer linear programs and use the FKG correlation inequality to derive an improved analysis of randomized rounding on them. This yields a pessimistic estimator, thus presenting deterministic polynomial-time algorithms for them with approximation guarantees that are significantly better than those known.

Computing with Very Weak Random Sources

Abstract: We give an efficient algorithm to extract randomness from a very weak random source using a small additional number t of truly random bits. Our work extends that of Nisan and Zuckerman [ J. Comput. System Sci., 52 (1996), pp. 43--52] in that t remains small even if the entropy rate is well below constant. A key application of this is in running randomized algorithms using such a very weak source of randomness. For any fixed $\gamma > 0$, we show how to simulate RP algorithms in time $n^{O(\log n)}$ using the output of a \ds\ with min-entropy $R^\gamma$. Such a weak random source is asked once for $R$ bits; it outputs an $R$-bit string according to any probability distribution that places probability at most $2^{-R^\gamma}$ on each string. If $\gamma > 1/2$, our simulation also works for BPP; for $\gamma > 1-1/(k+1)$, our simulation takes time $n^{O(\logk n)}$ (log(k) is the logarithm iterated k times). We also give a polynomial-time BPP simulation using Chor--Goldreich sources of min-entropy $R^{\Omega(1)}$, which is optimal. We present applications to time-space tradeoffs, expander constructions, and to the hardness of approximation. Of independent interest is our randomness-efficient Leftover Hash Lemma, a key tool for extracting randomness from weak random sources.

New algorithmic aspects of the Local Lemma with applications to routing and partitioning

Abstract: The Lovasz local lemma (LLL)is a powerful tool that is increasingly playing a valuable role in computer science. The original lemma was nonconstructive; a breakthrough of Beck and its generalizations (due to Alon and Molloy and Reed)have led to constructive versions. However, these methods do not capture some classes of applications of the LLL. We make progress on this by providing algorithmic approaches to two families of applications of the LLL. The first provides constructive versions of certain applications of an extension of the LLL (modeling, e.g., hypergraph-partitioning and low-congestion routing problems); the second provides new algorithmic results on constructing disjoint paths in graphs. Our results can also be seen as constructive upper bounds on the integrality gap of certain packing problems. One common theme of our work is a "gradual rounding" approach.

Low Discrepancy Sets Yield Approximate Min-Wise Independent Permutation Families

Abstract: Motivated by a problem of filtering near-duplicate Web documents, Broder, Charikar, Frieze & Mitzenmacher defined the following notion of e-approximate min-wise independent permutation families [2]. A multiset \(\mathcal{F}\) of permutations of {0,1, ... , n–1} is such a family if for all K ⊆ {0,1, ..., n–1} and any x ∈ K, a permutation π chosen uniformly at random form \(\mathcal{F}\) statisfies

Application-layer broker for scalable Internet services with resource reservation

Abstract: Scalability is a very important issue in providing Internet services, especially in view of the explosive growth in the number of Web users. When using the phrase Internet services, we consider text as well as multimedia presentations over the Internet, since accessing video and audio have become an integral part of the Web browsing activity. While this task of scalability can be considered as one of finding the best server or resource, the key issue of interest here is providing such a service in a transparent manner to the client. One such transparent approach is the Domain Name Server (DNS) proposed in [5]. This approach uses a modified DNS to distribute incoming client requests to different servers in a round-robin manner or based on a weighted classification. This allocation of client requests is done at the time of name-to-IP address translation carried out by the DNS. One limitation of this approach is that a translation request can go through a chain of intermediate DNSs that may cache the translation results. This caching might defeat the purpose of load balancing since an intermediate DNS can potentially allocate clients without the knowledge of the DNS in charge of load balancing. Another approach is to use a transparent front-end to forward requests to servers [4, 51. Cisco’s LocalDirector [4] is a product that uses address translation to forward requests to appropriate servers. The LocalDirector translates the headers of all data packets