]>
A Lower Bound on the Complexity of Approximate Nearest Neighbor Searching on the Hamming Cube
dcg-ann.pdf
Bernard Chazelle
Benjamin Gum
Alexey Lvov
STOC
1999 5
This paper considers Approximate Nearest Neighbor Searching (ANNS),
a basic problem of interest in a variety of areas ranging from
molecular biology to data mining. Using ideas inspired by
discrepancy theory, we establish the first query time lower bound on
deterministic ANNS algorithms, even on a very special space -- the
Hamming Cube -- and even if we require only very poor approximation.
A Lower Bound on the Complexity of Approximate Nearest Neighbor Searching on the Hamming Cube
dcg-ann.pdf
Bernard Chazelle
Benjamin Gum
Alexey Lvov
Discrete and Computational Geometry: The Goodman-Pollack
Festschrift, Springer-Verlag
2003 99
This paper considers Approximate Nearest Neighbor Searching (ANNS),
a basic problem of interest in a variety of areas ranging from
molecular biology to data mining. Using ideas inspired by
discrepancy theory, we establish the first query time lower bound on
deterministic ANNS algorithms, even on a very special space -- the
Hamming Cube -- and even if we require only very poor approximation.
Evasiveness of Subgraph Containment and Related Properties
sicomp-evasive.pdf
Subhash Khot
Yaoyun Shi
STACS
2001 2
In this paper we present some partial answers to the famous
conjecture that monotone graph properties are evasive. Adding new
group theoretic and number theoretic ideas to a previously known
topological method, we prove evasiveness of all minor-closed graph
properties. We significantly improve known results for subgraph
containment properties and for some generalizations.
Evasiveness of Subgraph Containment and Related Properties
sicomp-evasive.pdf
Subhash Khot
Yaoyun Shi
SIAM Journal on Computing 31(3)
2002 99
In this paper we present some partial answers to the famous
conjecture that monotone graph properties are evasive. Adding new
group theoretic and number theoretic ideas to a previously known
topological method, we prove evasiveness of all minor-closed graph
properties. We significantly improve known results for subgraph
containment properties and for some generalizations.
Improved Lower Bounds on the Randomized Complexity of Graph Properties
rsa-randglb.pdf
Subhash Khot
ICALP
2001 7
This paper considers the randomized decision tree complexity of
monotone properties of graphs. We improve the previous best
unconditional lower bound, using simple tools from probability
theory.
Improved Lower Bounds on the Randomized Complexity of Graph Properties
rsa-randglb.pdf
Subhash Khot
Random Structures and Algorithms 30(3)
2007 5
This paper considers the randomized decision tree complexity of
monotone properties of graphs. We improve the previous best
unconditional lower bound, using simple tools from probability
theory.
Informational Complexity and the Direct Sum Problem for
Simultaneous Message Complexity
focs01-infocomplex.pdf
Yaoyun Shi
Anthony Wirth
Andrew Yao
FOCS
2001 10
not occur. We also prove some
generalizations and extensions.
]]>
Improved Approximation Algorithms for Resource Allocation
ipco02-rap.pdf
Gruia Calinescu
Howard Karloff
Yuval Rabani
IPCO
2002 5
We consider the problem of selecting a maximum profit subset from a
given set of jobs such that the total resource requirement at no
point of time exceeds a given bound (this can be thought of as
maximum throughput scheduling). We give the current best constant
factor approximation.
Approximation Algorithms for the Unsplittable Flow Problem
algorithmica-ufp.pdf
Chandra Chekuri
Anupam Gupta
Amit Kumar
APPROX
2002 9
This paper studies the problem of routing, through a network, a
maximum profit subset of a given set of unsplittable flows, while
respecting all edge capacity constraints. We improve some earlier
results for expander networks and simplify others. We also obtain new
results for the line and ring networks.
Approximation Algorithms for the Unsplittable Flow Problem
algorithmica-ufp.pdf
Chandra Chekuri
Anupam Gupta
Amit Kumar
Algorithmica 47(1)
2007 2
This paper studies the problem of routing, through a network, a
maximum profit subset of a given set of unsplittable flows, while
respecting all edge capacity constraints. We improve some earlier
results for expander networks and simplify others. We also obtain new
results for the line and ring networks.
Near-Optimal Lower Bounds on the Multi-Party Communication
Complexity of Set Disjointness
ccc03-disj.pdf
Subhash Khot
Xiaodong Sun
CCC (Complexity)
2003 7
Suppose each of t players is given as input a subset of {1,2...,n}
with the promise that the t sets are either pairwise disjoint or
have an element in common but are otherwise pairwise disjoint. How
many bits of randomised communication are needed for them to
distinguish between these two cases? We establish lower bounds for
this problem that match the best known upper bounds, upto
logarithmic factors. The above problem has connections with the
computation of frequency moments for massive data in the streaming
model. Our communication lower bounds imply space lower bounds in
that model.
An Optimal Randomised Cell Probe Lower Bound for Approximate
Nearest Neighbour Searching
sicomp-randann.pdf
Oded Regev
FOCS
2004 10
We consider the approximate nearest neighbour search (ANNS) problem on
the d-dimensional Hamming cube. For polynomial storage and poly(d)
word size, we show matching lower and upper bounds on the number of
randomised queries required to solve ANNS. This closes a long line of
research on this basic and important problem.
An Optimal Randomised Cell Probe Lower Bound for Approximate
Nearest Neighbour Searching
sicomp-randann.pdf
Oded Regev
SIAM Journal on Computing 39(5)
2010 2
We consider the approximate nearest neighbour search (ANNS) problem on
the d-dimensional Hamming cube. For polynomial storage and poly(d)
word size, we show matching lower and upper bounds on the number of
randomised queries required to solve ANNS. This closes a long line of
research on this basic and important problem.
R*-Histograms: Efficient Representation of Spatial Relations
Between Objects of Arbitrary Topology
Yuhang Wang
Fillia Makedon
ACM Multimedia
2004 10
Yuhang's
page.
]]>
Estimating Entropy and Entropy Norm on Data Streams
imath-entropy-ds.pdf
Khanh Do_Ba
Shan Muthukrishnan
STACS
2006 2
A stream of m tokens, taken from a universe of size n (m >>
n), defines a empirical probability distribution. Several
applications in databases and network security need to summarize
such a distribution. Entropy and the related "entropy norm" are two
such summaries and particularly important ones because entropy is
central to information theory. In this work, we provide
space-efficient (sublinear space) algorithms to estimate these two
quantities and prove a space lower bound for estimation of the
entropy norm.
Estimating Entropy and Entropy Norm on Data Streams
imath-entropy-ds.pdf
Khanh Do_Ba
Shan Muthukrishnan
Internet Mathematics 3(1)
2006 99
A stream of m tokens, taken from a universe of size n (m >>
n), defines a empirical probability distribution. Several
applications in databases and network security need to summarize
such a distribution. Entropy and the related "entropy norm" are two
such summaries and particularly important ones because entropy is
central to information theory. In this work, we provide
space-efficient (sublinear space) algorithms to estimate these two
quantities and prove a space lower bound for estimation of the
entropy norm.
A Quasi-PTAS for Unsplittable Flow on Line Graphs
stoc06-ufp-qptas.pdf
Nikhil Bansal
Amir Epstein
Baruch Schieber
STOC
2006 5
We study the problem of routing multicommodity network flows on a
line network with non-uniform capacities and obtain a
quasi-polynomial-time approximation scheme for the max profit
routable subset of a given set of flow demands. Our algorithm also
extends to ring networks. These results improve upon earlier
(2+epsilon)-approximations. More importantly, they addresses the
long-standing open question of whether or not this problem is
APX-hard on lines and rings. Our results strongly indicate that it
is not.
Attack Detection in Time Series for Recommendation Systems
kdd06-attack.pdf
Sheng Zhang
Fillia Makedon
James Ford
KDD
2006 8
Details will be posted here in due course; please stand by.
Details will be posted here in due course; please stand by.
Details will be posted here in due course; please stand by.
A Near-Optimal Algorithm for Computing the Entropy of a Stream
talg-entropy-opt.pdf
Graham Cormode
Andrew McGregor
SODA
2007 1
optimal algorithm and we *prove* this near-optimality
via a lower bound. We also prove upper and lower bound results for
estimating a related quantity called the *k*th order entropy.
]]>
A Near-Optimal Algorithm for Estimating the Entropy of a Stream
talg-entropy-opt.pdf
Graham Cormode
Andrew McGregor
ACM Transactions on Algorithms 6(3)
2010 6
optimal algorithm and we *prove* this near-optimality
via a lower bound. We also prove upper and lower bound results for
estimating a related quantity called the *k*th order entropy.
]]>
Lower Bounds for Multi-Player Pointer Jumping
ccc07-mpj.pdf
CCC (Complexity)
2007 6
In the pointer jumping problem, a number of players who share an
input graph amongst themselves, must communicate to determine the
node reached by following pointers (i.e., directed edges) out of a
designated start node. This problem is considered a promising
candidate for resolving some long-standing open problems in circuit
complexity. Here, we make progress on these open problems by proving
large communication lower bounds for pointer jumping in certain
restricted models. The hope is that in future work the restrictions
can be relaxed to the point where we can derive nontrivial circuit
lower bounds.
Nearly Private Information Retrieval
mfcs07-apir.pdf
Anna Shubina
MFCS
2007 8
Coming soon. Please stand by.
Tight Lower Bounds for Selection in Randomly Ordered Streams
soda08-median-ds.pdf
T. S. Jayram
Mihai Patrascu
SODA
2008 1
We show that any algorithm computing the median of a stream
presented in random order, using $\polylog(n)$ space, requires an
optimal $\Omega(\log\log n)$ passes, resolving an open question from
the seminal paper on streaming by Munro and Paterson, from FOCS
1978.
Sublinear Communication Protocols for Multi-Party Pointer
Jumping and a Related Lower Bound
stacs08-mpj-ub.pdf
Joshua Brody
STACS
2008 2
sublinear communication protocol. Proving strong
lower bounds on MPJ is a long-standing challenge, and most
techniques developed so far were shooting for *linear* lower
bounds, and had succeeded in proving such lower bounds in somewhat
restricted models. Our result therefore shows that there is
something deep in the structure of MPJ that these earlier techniques
cannot tackle. We also consider a new restricted model for MPJ
(inspired by our upper bound) and prove a strong
*n* - O(log *n*) lower bound in this model.
]]>
Robust Lower Bounds for Communication and Stream Computation
stoc08-rcc.pdf
Graham Cormode
Andrew McGregor
STOC
2008 5
Communication complexity typically involves partitioning the input
to a problem amongst two (or more) players in a fixed way. But what
happens if the data are instead partitioned at random amongst the
players? When do traditionally hard problems become easy, and when
do lower bounds stay robust? We initiate a study of such questions.
A key motivation is that such random partition lower bounds apply
quite directly to data stream lower bounds where the input is
presented in random, rather than adversarial, order.
Embeddings, cuts, and flows in topological graphs: Lossy invariants, linearization, and 2-sums
focs08-planar.pdf
Alexander Jaffe
James Lee
Justin Vincent
FOCS
2008 10
Coming soon; please stand by.
Annotations in Data Streams
icalp09anno.pdf
Subsumed by more recent manuscript with same title, containing many more results
Graham Cormode
Andrew McGregor
ICALP
2009 7
Coming soon; please stand by.
Annotations in Data Streams
mscript-anno-stream.pdf
Graham Cormode
Andrew McGregor
Justin Thaler
ACM Transactions on Algorithms 11(1)
2014 10
Coming soon; please stand by.
Functional Monitoring Without Monotonicity
icalp09funcmon.pdf
Chrisil Arackaparambil
Joshua Brody
ICALP
2009 7
Coming soon; please stand by.
A Multi-Round Communication Lower Bound for Gap Hamming and Some Consequences
ccc09-ghd.pdf
http://eccc.hpi-web.de/eccc-reports/2009/TR09-015/index.html
http://arXiv.org/abs/0902.2399
Joshua Brody
CCC
2009 7.5
The communication problem of Gap-Hamming Distance (GHD) asks Alice and Bob to
tell whether their respective *n*-bit binary strings are *close*
(i.e., have Hamming distance less than *n*/2 - n^{1/2}) or
*far* (i.e., have Hamming distance greater than *n*/2 + n^{1/2}).
The problem is known to have a one-way randomized communication complexity of Omega(n)
and it was a long-standing open problem whether this extends to multi-round protocols.
In this paper, we resolve this question, showing that an Omega(n) bound indeed holds
for any constant number of rounds. This has applications to a number of data stream
computations, where tight one-pass space lower bounds can be extended to multi-pass
bounds as corollaries of our main result.
Combinatorial Theorems about Embedding Trees on the Real Line
jgt-lineembed.pdf
Subhash Khot
Journal of Graph Theory 67(2)
2011 6
Coming soon; please stand by.
Approximability of the Unsplittable Flow Problem on Trees
http://www.cs.dartmouth.edu/reports/abstracts/TR2009-642/
Chrisil Arackaparambil
Chien-Chung Huang
xxx
2009 6
Coming soon; please stand by.
Better Gap-Hamming Lower Bounds via Better Round Elimination
random10ghd.pdf
Joshua Brody
Oded Regev
Thomas Vidick
Ronald de Wolf
RANDOM
2010 9
In a CCC 2009 paper, we had shown the first nontrivial lower bound on the
multi-round communication complexity of GHD. In this paper, we greatly improve the
dependence of the bound on the number of rounds. To be precise, whereas the earlier
work bounded the maximum message length by Omega(n/exp(k^{2})), with
*k* being the number of rounds, we now improve this to roughly
Omega(n/k^{2}). The key insight is a more geometric approach to analysing
the problem, as opposed to the more purely combinatorial approach of the previous
work.
Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition
http://eccc.hpi-web.de/report/2010/076/
Graham Cormode
Ranganath Kondapally
Andrew McGregor
FOCS
2010 10
Coming soon; please stand by.
Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition
sicomp-pq.pdf
Graham Cormode
Ranganath Kondapally
Andrew McGregor
SIAM Journal on Computing 42(1)
2013 1
Coming soon; please stand by.
A Note on Randomized Streaming Space Bounds for the Longest Increasing Subsequence Problem
mscript-lis-ub.pdf
Information Processing Letters 112(7)
2012 1
Coming soon; please stand by.
An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance
sicomp-ghd-opt.pdf
Oded Regev
STOC
2011 6
Coming soon; please stand by.
An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance
sicomp-ghd-opt.pdf
Oded Regev
SIAM Journal on Computing 41(5)
2012 10
Coming soon; please stand by.
Everywhere-Tight Information Cost Tradeoffs for Augmented Index
random11augidx.pdf
Ranganath Kondapally
RANDOM
2011 8
Coming soon; please stand by.
An Improved Approximation Algorithm for Resource Allocation
ipco02-rap.pdf
Gruia Calinescu
Howard Karloff
Yuval Rabani
ACM Transactions on Algorithms 7(4)
2011 9
We consider the problem of selecting a maximum profit subset from a
given set of jobs such that the total resource requirement at no
point of time exceeds a given bound (this can be thought of as
maximum throughput scheduling). We give the current best constant
factor approximation.
When the Cut Condition is Enough: A Complete Characterization for Multiflow Problems in Series-Parallel Networks
stoc12spindle.pdf
Lisa Fleischer
Christophe Weibel
STOC
2012 5
Coming soon; please stand by.
The Query Complexity of Estimating Weighted Averages
http://www.springerlink.com/content/0k50n3176q2k0815/
Venkatesan Guruswami
Andrew Wirth
Anthony Wirth
Acta Informatica 48(7)
2011 12
Coming soon; please stand by.
Information Complexity versus Corruption and Applications to Orthogonality and Gap-Hamming
http://arxiv.org/abs/1205.0968
Ranganath Kondapally
Zhenghui Wang
RANDOM
2012 8
Coming soon; please stand by.
Annotations for Sparse Data Streams
http://arxiv.org/abs/1304.3816
Graham Cormode
Navin Goyal
Justin Thaler
SODA
2014 1
Coming soon; please stand by.
A Fast Streaming Spanner Algorithm for Incrementally Constructing Sparse Roadmaps
iros13-undir-roadmaps.pdf
Weifu Wang
Devin Balkcom
IROS
2013 11
Coming soon; please stand by.
Submodular Maximization Meets Streaming: Matchings, Matroids, and More
mathprog-submod-matching.pdf
Sagar Kale
IPCO
2014 6
Coming soon; please stand by.
Verifiable Stream Computation and Arthurâ€“Merlin Communication
sicomp-oip.pdf
Graham Cormode
Andrew McGregor
Justin Thaler
Suresh Venkatasubramanian
CCC
2015 6
Coming soon; please stand by.
Verifiable Stream Computation and Arthurâ€“Merlin Communication
sicomp-oip.pdf
Graham Cormode
Andrew McGregor
Justin Thaler
Suresh Venkatasubramanian
SIAM Journal on Computing 48(4)
2019 7
Coming soon; please stand by.
Beyond Set Disjointness: The Communication Complexity of Finding the Intersection
podc14-set-inter.pdf
Joshua Brody
Ranganath Kondapally
David Woodruff
Grigory Yaroslavtsev
PODC
2014 6
Coming soon; please stand by.
Certifying Equality With Limited Interaction
http://eccc.hpi-web.de/report/2012/153/
Joshua Brody
Ranganath Kondapally
David Woodruff
Grigory Yaroslavtsev
RANDOM
2014 9
Coming soon; please stand by.
A Depth-Five Lower Bound for Iterated Matrix Multiplication
ccc15-depth5imm.pdf
Suman K. Bera
CCC
2015 6
Coming soon; please stand by.
Submodular Maximization Meets Streaming: Matchings, Matroids, and More
mathprog-submod-matching.pdf
Sagar Kale
Mathematical Programming Series B 154(1)
2015 12
Coming soon; please stand by.
On Density, Threshold and Emptiness Queries for Intervals in the Streaming Model
TBD
Arijit Bishnu
Subhas Nandy
Sandeep Sen
FSTTCS
2015 12
Coming soon; please stand by.
Incidence Geometries and the Pass Complexity of Semi-Streaming Set Cover
http://eccc.hpi-web.de/report/2015/113/
Anthony Wirth
SODA
2016 1
Coming soon; please stand by.
Strong Fooling Sets for Multi-Player Communication with Applications to Deterministic Estimation of Stream Statistics
http://eccc.hpi-web.de/report/2016/111/
Sagar Kale
FOCS
2016 10
Coming soon; please stand by.
Certifying Equality With Limited Interaction
https://link.springer.com/article/10.1007/s00453-016-0163-6
Joshua Brody
Ranganath Kondapally
David Woodruff
Grigory Yaroslavtsev
Algorithmica 76(3)
2016 11
Coming soon; please stand by.
Towards Tighter Space Bounds for Counting Triangles and Other Substructures in Graph Streams
stacs17-triangles.pdf
Suman K. Bera
STACS
2017 2
Coming soon; please stand by.
Time-Space Tradeoffs for the Memory Game
https://arxiv.org/abs/1712.01330
Yining Chen
xxx
2017 12
Coming soon; please stand by.
Streaming Verification of Graph Computations via Graph Structure
random19-graphverif.pdf
Prantar Ghosh
RANDOM
2019 9
Coming soon; please stand by.
Vertex Ordering Problems in Directed Graph Streams
soda20-digraphstream.pdf
Andrew McGregor
Prantar Ghosh
Sofya Vorotnikova
SODA
2020 1
Coming soon; please stand by.
Graph Coloring via Degeneracy in Streaming and Other Space-Conscious Models
icalp20-stream-color.pdf
Suman K. Bera
Prantar Ghosh
ICALP
2020 7
coming soon; please stand by.
Streaming Verification of Graph Computations via Graph Structure
random20-graphverif-noncomm.pdf
Prantar Ghosh
Justin Thaler
RANDOM
2020 9
Coming soon; please stand by.
Adversarially Robust Coloring for Graph Streams
itcs22-robustcolor.pdf
Prantar Ghosh
Manuel Stoeckl
ITCS
2022 1
coming soon; please stand by.
The Element Extraction Problem and the Cost of Determinism and Limited Adaptivity in Linear Queries
https://arxiv.org/abs/2107.05810
Manuel Stoeckl
xxx
2021 7
Coming soon; please stand by.
Counting Simplices in Hypergraph Streams
https://drops.dagstuhl.de/opus/volltexte/2022/16970
Themistoklis Haris
ESA
2022 9
Coming soon; please stand by.