New Bounds for the CLIQUE-GAP Problem Using Graph Decomposition Theory

Braverman, Vladimir; Liu, Zaoxing; Singh, Tejasvam; Vinodchandran, N. V.; Yang, Lin F.

doi:10.1007/978-3-662-48054-0_13

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…Our work matches the lower bound for one-pass, and extends it to multiple-pass algorithms. The maximum independent set and maximum clique problems were also previously studied [24,36,50,50]; the known lower bounds also apply to these problems with a gap promise, so our construction is weaker in that sense. On the other hand, we improve upon the best results for maximum independent set [50] in a poly-logarithmic factor and in the simplicity of our construction, and on the results for maximum clique [24] in that we handle multiple-pass algorithms.…”

Section: Streaming Algorithmsmentioning

confidence: 99%

“…Finding an independent set matching this bound was studied in [50], and evaluating the value of the bound was recently studied in [36]; note that such a set might not be a maximum independent set. There is a variety of upper and lower bounds for the maximum independent set and maximum clique problems, under a gap assumption: either the graph contains a large independent set (clique), or only a very small one [24,51].…”

Section: Additional Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Smaller Cuts, Higher Lower Bounds

Abboud¹,

Censor-Hillel²,

Khoury³

et al. 2019

Preprint

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This paper proves strong lower bounds for distributed computing in the congest model, by presenting the bit-gadget: a new technique for constructing graphs with small cuts.The contribution of bit-gadgets is twofold. First, developing careful sparse graph constructions with small cuts extends known techniques to show a near-linear lower bound for computing the diameter, a result previously known only for dense graphs. Moreover, the sparseness of the construction plays a crucial role in applying it to approximations of various distance computation problems, drastically improving over what can be obtained when using dense graphs.Second, small cuts are essential for proving super-linear lower bounds, none of which were known prior to this work. In fact, they allow us to show near-quadratic lower bounds for several problems, such as exact minimum vertex cover or maximum independent set, as well as for coloring a graph with its chromatic number. Such strong lower bounds are not limited to NP-hard problems, as given by two simple graph problems in P which are shown to require a quadratic and near-quadratic number of rounds. All of the above are optimal up to logarithmic factors. In addition, in this context, the complexity of the all-pairs-shortestpaths problem is discussed.Finally, it is shown that graph constructions for congest lower bounds translate to lower bounds for the semi-streaming model, despite being very different in its nature.

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Section: Streaming Algorithmsmentioning

confidence: 99%

Section: Additional Related Workmentioning

confidence: 99%

Smaller Cuts, Higher Lower Bounds

Abboud¹,

Censor-Hillel²,

Khoury³

et al. 2019

Preprint

View full text Add to dashboard Cite

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BitMatrix: A Multipurpose Sketch for Monitoring of Multi-tenant Networks

2020

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One Sketch to Rule Them All

Liu

Manousis

Vorsanger

et al. 2016

Proceedings of the 2016 ACM SIGCOMM Conference

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389

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Network management requires accurate estimates of metrics for many applications including traffic engineering (e.g., heavy hitters), anomaly detection (e.g., entropy of source addresses), and security (e.g., DDoS detection). Obtaining accurate estimates given router CPU and memory constraints is a challenging problem. Existing approaches fall in one of two undesirable extremes: (1) low fidelity generalpurpose approaches such as sampling, or (2) high fidelity but complex algorithms customized to specific applicationlevel metrics. Ideally, a solution should be both general (i.e., supports many applications) and provide accuracy comparable to custom algorithms. This paper presents Univ-Mon, a framework for flow monitoring which leverages recent theoretical advances and demonstrates that it is possible to achieve both generality and high accuracy. UnivMon uses an application-agnostic data plane monitoring primitive; different (and possibly unforeseen) estimation algorithms run in the control plane, and use the statistics from the data plane to compute application-level metrics. We present a proofof-concept implementation of UnivMon using P4 and develop simple coordination techniques to provide a "one-bigswitch" abstraction for network-wide monitoring. We evaluate the effectiveness of UnivMon using a range of tracedriven evaluations and show that it offers comparable (and sometimes better) accuracy relative to custom sketching solutions across a range of monitoring tasks.

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New Bounds for the CLIQUE-GAP Problem Using Graph Decomposition Theory

Cited by 3 publications

References 17 publications

Smaller Cuts, Higher Lower Bounds

Smaller Cuts, Higher Lower Bounds

BitMatrix: A Multipurpose Sketch for Monitoring of Multi-tenant Networks

One Sketch to Rule Them All

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