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Submodular maximization meets streaming: matchings, matroids, and more

A general pattern for algorithms that maximize linear weight functions over “independent sets” is identified and it is proved that such algorithms can be adapted to maximize a submodular function.
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An optimal lower bound on the communication complexity of gap-hamming-distance

We prove an optimal Ω(n) lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space…
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Near-optimal lower bounds on the multi-party communication complexity of set disjointness

The results lead to an improved space complexity lower bound of /spl Omega/(n/sup 1-2/k//log n) for approximating the k/sup th/ frequency moment with a constant number of passes over the input, and a technical improvement if only one pass over theinput is permitted.
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Informational complexity and the direct sum problem for simultaneous message complexity

A new notion of informational complexity is introduced which is related to SM complexity and has nice direct sum properties and appears to be quite powerful and may be of independent interest.
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Approximation Algorithms for the Unsplittable Flow Problem

The main technique used for these results is randomized rounding followed by greedy alteration, and is inspired by the use of this idea in recent work.
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A quasi-PTAS for unsplittable flow on line graphs

A deterministic quasi-polynomial time approximation scheme for UFP on line graphs, thereby ruling out an APX-hardness result, unless NP ⊆ DTIME(2polylog(n)), which requires a quasi- polynomial bound on all edge capacities and demands in the input instance.
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Annotations in Data Streams

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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Improved Approximation Algorithms for Resource Allocation

It is shown that this NP-hard Resource Allocation problem can be (1/2-?)-approximated in polynomial time, which improves upon earlier approximation results for this problem.
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Functional Monitoring without Monotonicity

These are the first nontrivial algorithms for distributed monitoring of non-monotone functions when f is either H, the empirical Shannon entropy of a stream, or any of a related class of entropy functions (Tsallis entropies).
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An optimal randomised cell probe lower bound for approximate nearest neighbour searching

We consider the approximate nearest neighbour search problem on the Hamming cube {0, 1 }/sup d/. We show that a randomised cell probe algorithm that uses polynomial storage and word size d/sup O(1)/…
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