Funda Ergün

A note on the limits of collusion-resistant watermarks

In one proposed use of digital watermarks, the owner of a document D sells slightly different documents, D1;D2;,... to each buyer; if a buyer posts his/her document Di to the web, the owner can identify the source of the leak. More general attacks are however possible in which k buyers create some composite document D*; the goal of the owner is to identify at least one of the conspirators. We show, for a reasonable model of digital watermarks, fundamental limits on their efficacy against collusive attacks. In particular, if the effective document length is n, then at most O(√n= ln n) adversaries can defeat any watermarking scheme. Our attack is, in the theoretical model, oblivious to the watermarking scheme being used; in practice, it uses very little information about the watermarking scheme. Thus, using a proprietary system seems to give only a very weak defense.

QoS routing with performance-dependent costs

We study a network model in which each network link is associated with a set of delays and costs. These costs are a function of the delays and reflect the prices paid in return for delay guarantees. Such a cost structure can model a setting in which the service provider provides multiple service classes with a different price and delay guarantee for each class. We are given a source node s, a sink node t, and an end-to-end delay constraint D. Our aim is to choose an s-t path and determine a set of per link delay guarantees along this path so as to satisfy the constraint D while minimizing the total cost incurred. In the case where the s-t path is known, we aim to optimally partition the end-to-end delay constraint into link constraints along the path. We present approximation algorithms for both problems, since they are known to be NP-hard. Our algorithms guarantee to produce solutions that are within a factor 1+/spl epsiv/ of the optimal, where /spl epsiv/ is a parameter of our choice. The run times are polynomial in the input size and 1//spl epsiv/. We also provide a number of heuristics for the second problem and present simulation results. Previous work on related problems either focused on optimal solutions for special cost functions or on heuristics that have no performance guarantees. In contrast, we present provably good approximation algorithms and heuristics which apply to general cost functions.

A dynamic lookup scheme for bursty access patterns

The problem of fast address lookup is crucial to routing and thus has received considerable attention. Most of the work in this field has focused on improving the speed of individual accesses-independent from the underlying access pattern. Gupta et al. (2000) proposed an efficient data structure to exploit the bias in access pattern. This technique achieves faster lookups for more frequently accessed keys while bounding the worst case lookup time; in fact it is (near) optimal under constraints on worst case performance. However,it needs to be rebuilt periodically to reflect the changes in access patterns, which can be inefficient for bursty environments. In this paper we introduce a new dynamic data structure to exploit biases in the access pattern, which tend to change dynamically. Previous work shows that there are many circumstances under which access patterns change quickly. Our data structure, which we call the biased skip list (BSL), has a self-update mechanism which reflects the changes in the access patterns efficiently and immediately, without any need for rebuilding. It improves throughput while keeping the worst case access time bounded by that of the fastest (unbiased) schemes. We demonstrate the practicality of BSL by experiments on data with varying degrees of burstiness.

Oblivious string embeddings and edit distance approximations

We introduce an oblivious embedding that maps strings of length <i>n</i> under edit distance to strings of length at most <i>n/r</i> under edit distance for any value of parameter <i>r.</i> For any given <i>r</i>, our embedding provides a distortion of <i>Õ</i>(<i>r</i>^1+μ) for some μ = <i>o</i>(1), which we prove to be (almost) optimal. The embedding can be computed in <i>Õ</i>(2^1/μ<i>n</i>) time.We also show how to use the main ideas behind the construction of our embedding to obtain an efficient algorithm for approximating the edit distance between two strings. More specifically, for any 1 > ε ≥ 0, we describe an algorithm to compute the edit distance <i>D(S, R)</i> between two strings <i>S</i> and <i>R</i> of length <i>n</i> in time <i>Õ</i>(<i>n</i>^1+ε), within an approximation factor of min{<i>n</i>^{1-ε/3+<i>o</i>(1)}, (<i>D</i>(<i>S</i>, <i>R</i>/<i>n</i>^ε)^{1/2+<i>o</i>(1)}}. For the case of ε = 0, we get a <i>Õ(n)</i>-time algorithm that approximates the edit distance within a factor of min{<i>n</i>^{1/3+<i>o</i>(1)}, <i>D(S, R)</i>^{1/2+<i>o</i>(1)}}, improving the recent result of Bar-Yossef et al. [2].

Online Load Balancing for MapReduce with Skewed Data Input

MapReduce has emerged as a powerful tool for distributed and scalable processing of voluminous data. In this paper, we, for the first time, examine the problem of accommodating data skew in MapReduce with online operations. Different from earlier heuristics in the very late reduce stage or after seeing all the data, we address the skew from the beginning of data input, and make no assumption about a priori knowledge of the data distribution nor require synchronized operations. We examine the input in a continuous fashion and adaptively assign tasks with a load-balanced strategy. We show that the optimal strategy is a constrained version of online minimum makespan and, in the MapReduce context where pairs with identical keys must be scheduled to the same machine, there is an online algorithm with a provable 2-competitive ratio. We further suggest a sample-based enhancement, which, probabilistically, achieves a 3/2-competitive ratio with a bounded error.

Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time

We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in

Comparing Sequences with Segment Rearrangements

\mathbb R^d

On learning bounded-width branching programs

. We focus on the setting where the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within

Periodicity in streams

1 + \eps

Fast approximate PCPs

using only