Publications (331)38.67 Total impact
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ABSTRACT: We study balanced circle packings and circlecontact representations for planar graphs, where the ratio of the largest circle's diameter to the smallest circle's diameter is polynomial in the number of circles. We provide a number of positive and negative results for the existence of such balanced configurations.08/2014;  [Show abstract] [Hide abstract]
ABSTRACT: Many wellknown graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings ubiquitously use iterative numerical approximations rather than constructing and then solving algebraic expressions representing their exact solutions. To explain this phenomenon, we use Galois theory to show that many variants of these problems have solutions that cannot be expressed by nested radicals or nested roots of lowdegree polynomials. Hence, such solutions cannot be computed exactly even in extended computational models that include such operations.08/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We study wearleveling techniques for cuckoo hashing, showing that it is possible to achieve a memory wear bound of $\log\log n+O(1)$ after the insertion of $n$ items into a table of size $Cn$ for a suitable constant $C$ using cuckoo hashing. Moreover, we study our cuckoo hashing method empirically, showing that it significantly improves on the memory wear performance for classic cuckoo hashing and linear probing in practice.04/2014; 
Article: Spinthebottle Sort and Annealing Sort: Oblivious Sorting via Roundrobin Random Comparisons.
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ABSTRACT: We study sorting algorithms based on randomized roundrobin comparisons. Specifically, we study Spinthebottle sort, where comparisons are unrestricted, and Annealing sort, where comparisons are restricted to a distance bounded by a temperature parameter. Both algorithms are simple, randomized, dataoblivious sorting algorithms, which are useful in privacypreserving computations, but, as we show, Annealing sort is much more efficient. We show that there is an input permutation that causes Spinthebottle sort to require Ω(n (2) log n) expected time in order to succeed, and that in O(n (2) log n) time this algorithm succeeds with high probability for any input. We also show there is a specification of Annealing sort that runs in O(n log n) time and succeeds with very high probability.Algorithmica 03/2014; 68(4):835858. · 0.49 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a simple, efficient, and secure dataoblivious randomized shuffle algorithm. This is the first secure dataoblivious shuffle that is not based on sorting. Our method can be used to improve previous oblivious storage solutions for networkbased outsourcing of data.02/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In streamed graph drawing, a planar graph, G, is given incrementally as a data stream and a straightline drawing of G must be updated after each new edge is released. To preserve the mental map, changes to the drawing should be minimized after each update, and Binucci et al.show that exponential area is necessary and sufficient for a number of streamed graph drawings for trees if edges are not allowed to move at all. We show that a number of streamed graph drawings can, in fact, be done with polynomial area, including planar streamed graph drawings of trees, treemaps, and outerplanar graphs, if we allow for a small number of coordinate movements after each update. Our algorithms involve an interesting connection to a classic algorithmic problem  the file maintenance problem  and we also give new algorithms for this problem in a framework where bulk memory moves are allowed.08/2013;  [Show abstract] [Hide abstract]
ABSTRACT: We study a threedimensional analogue to the wellknown graph visualization approach known as arc diagrams. We provide several algorithms that achieve good angular resolution for 3D arc diagrams, even for cases when the arcs must project to a given 2D straightline drawing of the input graph. Our methods make use of various graph coloring algorithms, including an algorithm for a new coloring problem, which we call localized edge coloring.08/2013; 
Article: SetDifference Range Queries
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ABSTRACT: We introduce the problem of performing setdifference range queries, where answers to queries are settheoretic symmetric differences between sets of items in two geometric ranges. We describe a general framework for answering such queries based on a novel use of datastreaming sketches we call signed symmetricdifference sketches. We show that such sketches can be realized using invertible Bloom filters (IBFs), which can be composed, differenced, and searched so as to solve setdifference range queries in a wide range of scenarios.06/2013;  [Show abstract] [Hide abstract]
ABSTRACT: Parametric search has been widely used in geometric algorithms. Cole's improvement provides a way of saving a logarithmic factor in the running time over what is achievable using the standard method. Unfortunately, this improvement comes at the expense of making an already complicated algorithm even more complex; hence, this technique has been mostly of theoretical interest. In this paper, we provide an algorithm engineering framework that allows for the same asymptotic complexity to be achieved probabilistically in a way that is both simple and practical (i.e., suitable for actual implementation). The main idea of our approach is to show that a variant of quicksort, known as boxsort, can be used to drive comparisons, instead of using a sorting network, like the complicated AKS network, or an EREW parallel sorting algorithm, like the fairly intricate parallel mergesort algorithm. This results in a randomized optimization algorithm with a running time matching that of using Cole's method, with high probability, while also being practical. We show how this results in practical implementations of some geometric algorithms utilizing parametric searching and provide experimental results that prove practicality of the method.06/2013;  [Show abstract] [Hide abstract]
ABSTRACT: We formalize a problem we call combinatorial pair testing (CPT), which has applications to the identification of uncooperative or unproductive participants in pair programming, massively distributed computing, and crowdsourcing environments. We give efficient adaptive and nonadaptive CPT algorithms and we show that our methods use an optimal number of testing rounds to within constant factors. We also provide an empirical evaluation of some of our methods.05/2013;  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we study sparsityexploiting Mastermind algorithms for attacking the privacy of an entire database of character strings or vectors, such as DNA strings, movie ratings, or social network friendship data. Based on reductions to nonadaptive group testing, our methods are able to take advantage of minimal amounts of privacy leakage, such as contained in a single bit that indicates if two people in a medical database have any common genetic mutations, or if two people have any common friends in an online social network. We analyze our Mastermind attack algorithms using theoretical characterizations that provide sublinear bounds on the number of queries needed to clone the database, as well as experimental tests on genomic information, collaborative filtering data, and online social networks. By taking advantage of the generally sparse nature of these realworld databases and modulating a parameter that controls query sparsity, we demonstrate that relatively few nonadaptive queries are needed to recover a large majority of each database.IEEE Transactions on Knowledge and Data Engineering 01/2013; 25(1):131144. · 1.89 Impact Factor 
Conference Paper: Computing betweenness centrality in external memory
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ABSTRACT: Betweenness centrality is one of the most wellknown measures of the importance of nodes in a socialnetwork graph. In this paper we describe the first known externalmemory and cacheoblivious algorithms for computing betweenness centrality. We present four different externalmemory algorithms exhibiting various tradeoffs with respect to performance. Two of the algorithms are cacheoblivious. We describe general algorithms for networks with weighted and unweighted edges and a specialized algorithm for networks with small diameters, as is common in social networks exhibiting the “small worlds” phenomenon.Big Data, 2013 IEEE International Conference on; 01/2013 
Conference Paper: More graph drawing in the cloud: dataoblivious stnumbering, visibility representations, and orthogonal drawing of biconnected planar graphs
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ABSTRACT: We give a new efficient dataoblivious PRAM simulation and several new dataoblivious graphdrawing algorithms with application to privacypreserving graphdrawing in a cloud computing context.Proceedings of the 20th international conference on Graph Drawing; 09/2012 
Conference Paper: Graph drawing in the cloud: privately visualizing relational data using small working storage
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ABSTRACT: We study graph drawing in a cloudcomputing context where data is stored externally and processed using a small local working storage. We show that a number of classic graph drawing algorithms can be efficiently implemented in such a framework where the client can maintain privacy while constructing a drawing of her graph.Proceedings of the 20th international conference on Graph Drawing; 09/2012 
Conference Paper: On the density of maximal 1planar graphs
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ABSTRACT: A graph is 1planar if it can be drawn in the plane such that each edge is crossed at most once. It is maximal 1planar if the addition of any edge violates 1planarity. Maximal 1planar graphs have at most 4n−8 edges. We show that there are sparse maximal 1planar graphs with only $\frac{45}{17} n + \mathcal{O}(1)$ edges. With a fixed rotation system there are maximal 1planar graphs with only $\frac{7}{3} n + \mathcal{O}(1)$ edges. This is sparser than maximal planar graphs. There cannot be maximal 1planar graphs with less than $\frac{21}{10} n  \mathcal{O}(1)$ edges and less than $\frac{28}{13} n  \mathcal{O}(1)$ edges with a fixed rotation system. Furthermore, we prove that a maximal 1planar rotation system of a graph uniquely determines its 1planar embedding.Proceedings of the 20th international conference on Graph Drawing; 09/2012  [Show abstract] [Hide abstract]
ABSTRACT: Forcedirected layout algorithms produce graph drawings by resolving a system of emulated physical forces. We present techniques for using social gravity as an additional force in forcedirected layouts, together with a scaling technique, to produce drawings of trees and forests, as well as more complex social networks. Social gravity assigns mass to vertices in proportion to their network centrality, which allows vertices that are more graphtheoretically central to be visualized in physically central locations. Scaling varies the gravitational force throughout the simulation, and reduces crossings relative to unscaled gravity. In addition to providing this algorithmic framework, we apply our algorithms to social networks produced by Mark Lombardi, and we show how social gravity can be incorporated into forcedirected Lombardistyle drawings.09/2012;  [Show abstract] [Hide abstract]
ABSTRACT: We study graph drawing in a cloudcomputing context where data is stored externally and processed using a small local working storage. We show that a number of classic graph drawing algorithms can be efficiently implemented in such a framework where the client can maintain privacy while constructing a drawing of her graph.09/2012;  [Show abstract] [Hide abstract]
ABSTRACT: We study the question of how to shuffle $n$ cards when faced with an opponent who knows the initial position of all the cards {\em and} can track every card when permuted, {\em except} when one takes $K< n$ cards at a time and shuffles them in a private buffer "behind your back," which we call {\em buffer shuffling}. The problem arises naturally in the context of parallel mixnet servers as well as other security applications. Our analysis is based on related analyses of loadbalancing processes. We include extensions to variations that involve corrupted servers and adversarially injected messages, which correspond to an opponent who can peek at some shuffles in the buffer and who can mark some number of the cards. In addition, our analysis makes novel use of a sumofsquares metric for anonymity, which leads to improved performance bounds for parallel mixnets and can also be used to bound wellknown existing anonymity measures.05/2012;  [Show abstract] [Hide abstract]
ABSTRACT: Searching accounts for one of the most frequently performed computations over the Internet as well as one of the most important applications of outsourced computing, producing results that critically affect users' decisionmaking behaviors. As such, verifying the integrity of Internetbased searches over vast amounts of web contents is essential. We provide the first solution to this general security problem. We introduce the concept of an authenticated web crawler and present the design and prototype implementation of this new concept. An authenticated web crawler is a trusted program that computes a special "signature" $s$ of a collection of web contents it visits. Subject to this signature, web searches can be verified to be correct with respect to the integrity of their produced results. This signature also allows the verification of complicated queries on web pages, such as conjunctive keyword searches. In our solution, along with the web pages that satisfy any given search query, the search engine also returns a cryptographic proof. This proof, together with the signature $s$, enables any user to efficiently verify that no legitimate web pages are omitted from the result computed by the search engine, and that no pages that are nonconforming with the query are included in the result. An important property of our solution is that the proof size and the verification time both depend solely on the sizes of the query description and the query result, but not on the number or sizes of the web pages over which the search is performed. Our authentication protocols are based on standard Merkle trees and the more involved bilinearmap accumulators. As we experimentally demonstrate, the prototype implementation of our system gives a low communication overhead between the search engine and the user, and allows for fast verification of the returned results on the user side.04/2012; 
Article: Practical oblivious storage
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ABSTRACT: We study oblivious storage (OS), a natural way to model privacypreserving data outsourcing where a client, Alice, stores sensitive data at an honestbutcurious server, Bob. We show that Alice can hide both the content of her data and the pattern in which she accesses her data, with high probability, using a method that achieves O(1) amortized rounds of communication between her and Bob for each data access. We assume that Alice and Bob exchange small messages, of size O(N1/c), for some constant c>=2, in a single round, where N is the size of the data set that Alice is storing with Bob. We also assume that Alice has a private memory of size 2N1/c. These assumptions model realworld cloud storage scenarios, where tradeoffs occur between latency, bandwidth, and the size of the client's private memory.01/2012;
Publication Stats
5k  Citations  
38.67  Total Impact Points  
Top Journals
Institutions

2000–2014

University of California, Irvine
 • Department of Computer Science
 • Secure Computing and Networking Center (SCONCE)
Irvine, California, United States 
University of Waterloo
Waterloo, Ontario, Canada


2008

UC Irvine Health
Santa Ana, California, United States


1988–2006

Johns Hopkins University
 Department of Computer Science
Baltimore, MD, United States


1999

Technion  Israel Institute of Technology
H̱efa, Haifa District, Israel


1997

The University of Memphis
 Department of Mathematical Sciences
Memphis, Tennessee, United States


1994

Texas A&M University
 Department of Computer Science and Engineering
College Station, TX, United States


1986–1990

Purdue University
 Department of Computer Science
West Lafayette, IN, United States


1970

Stanford University
 Department of Computer Science
Palo Alto, CA, United States
