
Robust Lower Bounds for Graph Problems in the Blackboard Model of Communication
We give lower bounds on the communication complexity of graph problems i...
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Lower Bounds for the Happy Coloring Problems
In this paper, we study the Maximum Happy Vertices and the Maximum Happy...
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Streaming Frequent Items with Timestamps and Detecting Large Neighborhoods in Graph Streams
Detecting frequent items is a fundamental problem in data streaming rese...
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Maximum Matchings and Minimum Blocking Sets in Θ_6Graphs
Θ_6Graphs are important geometric graphs that have many applications es...
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Factorial Lower Bounds for (Almost) Random Order Streams
In this paper we introduce and study the StreamingCycles problem, a rand...
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A modified greedy algorithm to improve bounds for the vertex cover number
In any attempt at designing an efficient algorithm for the minimum verte...
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An Optimal Algorithm for Triangle Counting
We present a new algorithm for approximating the number of triangles in ...
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Optimal Lower Bounds for Matching and Vertex Cover in Dynamic Graph Streams
In this paper, we give simple optimal lower bounds on the oneway twoparty communication complexity of approximate Maximum Matching and Minimum Vertex Cover with deletions. In our model, Alice holds a set of edges and sends a single message to Bob. Bob holds a set of edge deletions, which form a subset of Alice's edges, and needs to report a large matching or a small vertex cover in the graph spanned by the edges that are not deleted. Our results imply optimal space lower bounds for insertiondeletion streaming algorithms for Maximum Matching and Minimum Vertex Cover. Previously, Assadi et al. [SODA 2016] gave an optimal space lower bound for insertiondeletion streaming algorithms for Maximum Matching via the simultaneous model of communication. Our lower bound is simpler and stronger in several aspects: The lower bound of Assadi et al. only holds for algorithms that (1) are able to process streams that contain a triple exponential number of deletions in n, the number of vertices of the input graph; (2) are able to process multigraphs; and (3) never output edges that do not exist in the input graph when the randomized algorithm errs. In contrast, our lower bound even holds for algorithms that (1) rely on short (O(n^2)length) input streams; (2) are only able to process simple graphs; and (3) may output nonexisting edges when the algorithm errs.
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