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Towards a Theory of Parameterized Streaming Algorithms

Rajesh Chitnis, Graham Cormode, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
In this paper, we initiate a systematic study of graph problems from the paradigm of parameterized streaming algorithms.  ...  On the hardness side, we obtain lower bounds for the parameterized streaming complexity of various problems via novel reductions from problems in communication complexity.  ...  In this paper we consider streaming algorithms for graph problems over fixed vertex sets, where information about the edges arrives edge by edge [29] .  ... 
doi:10.4230/lipics.ipec.2019.7 dblp:conf/iwpec/ChitnisC19 fatcat:c4qnqaa6bnf5lhbh5dp33uf6hi

Towards a Theory of Parameterized Streaming Algorithms [article]

Rajesh Chitnis, Graham Cormode
2019 arXiv   pre-print
In this paper, we initiate a systematic study of graph problems from the paradigm of parameterized streaming algorithms.  ...  [SODA'15] introduced the notions of streaming kernels and parameterized streaming algorithms respectively.  ...  Formally, we say that a problem is fixed-parameter tractable (FPT) with respect to parameter k if the problem can be solved in time f (k) · n O (1) where f is a computable function and n is the input  ... 
arXiv:1911.09650v1 fatcat:yvbpw6rsunbcrl3zezonsscf7a

Parameterized Streaming Algorithms for Vertex Cover [article]

Rajesh Chitnis, Graham Cormode, MohammadTaghi Hajiaghayi, Morteza Monemizadeh
2014 arXiv   pre-print
However, few results are known for optimization problems over such dynamic graph streams.  ...  In this paper, we introduce a new approach to handling graph streams, by instead seeking solutions for the parameterized versions of these problems where we are given a parameter k and the objective is  ...  We thank Catalin Tiseanu for some useful discussions regarding the Feedback Vertex Set problem.  ... 
arXiv:1405.0093v2 fatcat:4mqzunoomvdahi3kbssuvf7cjy

As Time Goes By: Reflections on Treewidth for Temporal Graphs [chapter]

Till Fluschnik, Hendrik Molter, Rolf Niedermeier, Malte Renken, Philipp Zschoche
2020 Lecture Notes in Computer Science  
Treewidth is arguably the most important structural graph parameter leading to algorithmically beneficial graph decompositions.  ...  Triggered by a strongly growing interest in temporal networks (graphs where edge sets change over time), we discuss fresh algorithmic views on temporal tree decompositions and temporal treewidth.  ...  Mertzios for their constructive feedback which helped us to improve the presentation of the paper.  ... 
doi:10.1007/978-3-030-42071-0_6 fatcat:wutcqkgkbvb3jojzndezrti6ky

Parameterized Streaming: Maximal Matching and Vertex Cover [chapter]

Rajesh Chitnis, Graham Cormode, Mohammad Taghi Hajiaghayi, Morteza Monemizadeh
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
However, few results are known for optimization problems over such dynamic graph streams.  ...  In this paper, we introduce a new approach to handling graph streams, by instead seeking solutions for the parameterized versions of these problems.  ...  We thank Catalin Stefan Tiseanu for some useful discussions regarding the Feedback Vertex Set problem.  ... 
doi:10.1137/1.9781611973730.82 dblp:conf/soda/ChitnisCHM15 fatcat:jtavw3arf5cpdemr76lym677ym

A Parameterized View on Matroid Optimization Problems [chapter]

Dániel Marx
2006 Lecture Notes in Computer Science  
Here we investigate these problems from the parameterized complexity point of view: instead of the trivial n O(k) time brute force algorithm for finding a k-element solution, we try to give algorithms  ...  As consequence, algorithms with similar running time are obtained for other problems such as finding a k-element set in the intersection of ℓ matroids, or finding k terminals in a network such that each  ...  Therefore, Theorem 1.1 can be used to solve the problem. Acknowledgments I'm grateful to Lajos Rónyai for his useful comments on the paper.  ... 
doi:10.1007/11786986_57 fatcat:etbmvqm6tfgkvh5t5gywnx7f5e

A parameterized view on matroid optimization problems

Dániel Marx
2009 Theoretical Computer Science  
Here we investigate these problems from the parameterized complexity point of view: instead of the trivial n O(k) time brute force algorithm for finding a k-element solution, we try to give algorithms  ...  As a consequence, algorithms with similar running time are obtained for other problems such as finding a k-element set in the intersection of matroids, or finding k terminals in a network such that each  ...  Many NP-hard problems were investigated in the parameterized complexity literature, with the goal of identifying fixed-parameter tractable problems.  ... 
doi:10.1016/j.tcs.2009.07.027 fatcat:z3yxvjhepner5a4gse65o2usgq

Structural Parameterization for Graph Deletion Problems over Data Streams [article]

Arijit Bishnu and Arijit Ghosh and Sudeshna Kolay and Gopinath Mishra and Saket Saurabh
2019 arXiv   pre-print
We focus on the vertex cover size K as the parameter for the parameterized graph deletion problems we consider.  ...  The study of parameterized streaming complexity on graph problems was initiated by Fafianie et al. (MFCS'14) and Chitnis et al. (SODA'15 and SODA'16).  ...  Conclusion In this paper, we initiate the study of parameterized streaming complexity with structural parameters for graph deletion problems.  ... 
arXiv:1906.05458v2 fatcat:cmne5hu34rgohatqv2il7kayay

Multistage Vertex Cover

Till Fluschnik, Rolf Niedermeier, Valentin Rohm, Philipp Zschoche, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
On the positive side, however, we also spot several fixed-parameter tractability results based on some of the most natural parameterizations.  ...  We will study its parameterized complexity regarding the problem-specific parameters k, τ , , and some of their combinations, as well as restrictions to temporal graph classes [13] .  ...  [22] used a similar configuration graph to show fixed-parameter tractability of Vertex Cover Reconfiguration parameterized by the vertex cover size k.  ... 
doi:10.4230/lipics.ipec.2019.14 dblp:conf/iwpec/FluschnikNRZ19 fatcat:xbl7x2heqjfuph5ih34lpszd2m

Tradeoffs in Backdoors: Inconsistency Detection, Dynamic Simplification, and Preprocessing

Bistra Dilkina, Carla P. Gomes, Ashish Sabharwal
2008 International Symposium on Artificial Intelligence and Mathematics  
There has been considerable interest in the identification of structural properties of combinatorial problems that lead to efficient algorithms for solving them.  ...  We prove that strong backdoor identification with respect to the tractable classes Horn and 2CNF becomes harder than NP (unless NP=coNP) as soon as the inconsequential sounding feature of empty clause  ...  is shown to be fixed parameter tractable.  ... 
dblp:conf/isaim/DilkinaGS08 fatcat:y4azywhilrclfabs6w2bwdptgu

Fractals for Kernelization Lower Bounds [article]

Till Fluschnik, Danny Hermelin, André Nichterlein, Rolf Niedermeier
2017 arXiv   pre-print
such that the resulting graph has no s-t path of length shorter than ℓ) parameterized by the combination of k and ℓ has no polynomial-size problem kernel.  ...  Our framework applies to planar as well as directed variants of the basic problems and also applies to both edge and vertex deletion problems.  ...  Unless NP ⊆ coNP / poly, Minimum Diameter Edge Deletion on directed planar graphs parameterized by (k, ℓ) does not admit a polynomial kernel. Proof (Sketch).  ... 
arXiv:1512.00333v3 fatcat:yfxcjd5q7fa2tbev7ud7we6ovy

Streaming Kernelization [article]

Stefan Fafianie, Stefan Kratsch
2014 arXiv   pre-print
Kernelization is a formalization of preprocessing for combinatorially hard problems.  ...  We obtain several results in this new setting, depending on the number of passes over the input that such a streaming kernelization is allowed to make.  ...  A parameterized problem is fixed-parameter tractable if there is an algorithm that decides if (x, k) ∈ Q in f (k)|x| O(1) time, where f is any computable function.  ... 
arXiv:1405.1356v1 fatcat:cbi4l3cienegbhgrpgxcs2e4na

Streaming Kernelization [chapter]

Stefan Fafianie, Stefan Kratsch
2014 Lecture Notes in Computer Science  
We obtain several results in this new setting, depending on the number of passes over the input that such a streaming kernelization is allowed to make.  ...  Kernelization is a formalization of preprocessing for combinatorially hard problems.  ...  A parameterized problem is fixed-parameter tractable if there is an algorithm that decides if (x, k) ∈ Q in f (k)|x| O(1) time, where f is any computable function.  ... 
doi:10.1007/978-3-662-44465-8_24 fatcat:4raifqfmzjfftppjz5jc7rexiy

Multistage Vertex Cover [article]

Till Fluschnik, Rolf Niedermeier, Valentin Rohm, Philipp Zschoche
2020 arXiv   pre-print
On the positive side, however, we also spot several fixed-parameter tractability results based on some of the most natural parameterizations.  ...  Covering all edges of a graph by a small number of vertices, this is the NP-complete Vertex Cover problem. It is among the most fundamental graph-algorithmic problems.  ...  We leave open whether Multistage Vertex Cover parameterized by k is fixed-parameter tractable when each layer consists of only one edge (see Table 1 ).  ... 
arXiv:1906.00659v3 fatcat:jghp53ausjhchawz5lq3ni44jm

EVOLVING INSIDER THREAT DETECTION STREAM MINING PERSPECTIVE

PALLABI PARVEEN, NATHAN MCDANIEL, ZACKARY WEGER, JONATHAN EVANS, BHAVANI THURAISINGHAM, KEVIN HAMLEN, LATIFUR KHAN
2013 International journal on artificial intelligence tools  
Evidence of malicious insider activity is often buried within large data streams, such as system logs accumulated over months or years.  ...  This paper applies ensemble-based stream mining, supervised and unsupervised learning, and graph-based anomaly detection to the problem of insider threat detection.  ...  This work is supported by the Air Force Office of Scientific Research, under grant FA9550-08-1-0088.  ... 
doi:10.1142/s0218213013600130 fatcat:qntmuz7zrjaanl56qfaajvcrra
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