In this paper, we present near-optimal space bounds for Lpsamplers. Given a stream of updates (additions and subtraction) to the coordinates of an underlying vector x ∈
Abstract. We present three streaming algorithms that ( , δ)− approximate 1 the number of triangles in graphs. Similar to the previous algorithms [3], the space usage of presented algorithms are inversely proportional to the number of triangles while, for some families of graphs, the space usage is improved. We also prove a lower bound, based on the number of triangles, which indicates that our first algorithm behaves almost optimally on graphs with constant degrees.
In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with m edges and at least T triangles, we show that an extra look over the stream yields a two-pass streaming algorithm that uses O(polylog(m)) space and outputs a (1 + ε) approximation of the number of triangles in the graph. This improves upon the two-pass streaming tester of Braverman, Ostrovsky and Vilenchik, ICALP 2013, which distinguishes between triangle-free graphs and graphs with at least T triangle using O( m T 1/3 ) space. Also, in terms of dependence on T , we show that more passes would not lead to a better space bound. In other words, we prove there is no constant pass streaming algorithm that distinguishes between triangle-free graphs from graphs with at least T triangles using O( m T 1/2+ρ ) space for any constant ρ ≥ 0.
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