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Optimizing linear counting queries under differential privacy

TLDR
The matrix mechanism is proposed, a new algorithm for answering a workload of predicate counting queries and the problem of computing the optimal query strategy in support of a given workload can be formulated as a rank-constrained semidefinite program.
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Analyzing graph structure via linear measurements

TLDR
The study of graph sketching is initiated, i.e., algorithms that use a limited number of linear measurements of a graph to determine the properties of the graph are studied, including the first dynamic graph semi-streaming algorithms for connectivity, spanning trees, sparsification, and matching problems.
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Finding Graph Matchings in Data Streams

TLDR
Algorithm for finding large graph matchings in the streaming model, applicable when dealing with massive graphs, edges are streamed-in in some arbitrary order rather than residing in randomly accessible memory, achieves a $\frac1{1+\epsilon}$ approximation for maximum cardinality matching and a $1+2$ approximation to maximum weighted matching.
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Graph sketches: sparsification, spanners, and subgraphs

TLDR
This work investigates graph sketching where the graphs of interest encode the relationships between these entities and considers properties of graphs including the size of the cuts, the distances between nodes, and the prevalence of dense sub-graphs.
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Graph stream algorithms: a survey

TLDR
The techniques developed in this area are now finding applications in other areas including data structures for dynamic graphs, approximation algorithms, and distributed and parallel computation.
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On graph problems in a semi-streaming model

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Reconstructing strings from random traces

TLDR
A study of deletion rates for which one can successfully reconstruct the original string using a small number of samples, and a simple reconstruction algorithm called Bitwise Majority Alignment has an interesting self-correcting property whereby local distortions in the traces do not generate errors in the reconstruction and eventually get corrected.
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Approximation algorithms for clustering uncertain data

TLDR
The core mining problem of clustering on uncertain data is studied, and appropriate natural generalizations of standard clustering optimization criteria are defined, and a variety of bicriteria approximation algorithms are shown, including the first known guaranteed approximation algorithms for the problems of clustered uncertain data.
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The matrix mechanism: optimizing linear counting queries under differential privacy

TLDR
The matrix mechanism, an algorithm for answering a workload of linear counting queries that adapts the noise distribution to properties of the provided queries, is described and it is shown that this problem can be formulated as a rank-constrained semidefinite program.
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Annotations in Data Streams

TLDR
Upper bounds are shown that achieve a nontrivial tradeoff between the amount of annotation used and the space required to verify it and lower bounds are proved, often nearly matching the upper bounds, via notions related to Merlin-Arthur communication complexity.
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