11,424 research outputs found
Lower Bounds for Structuring Unreliable Radio Networks
In this paper, we study lower bounds for randomized solutions to the maximal
independent set (MIS) and connected dominating set (CDS) problems in the dual
graph model of radio networks---a generalization of the standard graph-based
model that now includes unreliable links controlled by an adversary. We begin
by proving that a natural geographic constraint on the network topology is
required to solve these problems efficiently (i.e., in time polylogarthmic in
the network size). We then prove the importance of the assumption that nodes
are provided advance knowledge of their reliable neighbors (i.e, neighbors
connected by reliable links). Combined, these results answer an open question
by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC
2011] are optimal with respect to their dual graph model assumptions. They also
provide insight into what properties of an unreliable network enable efficient
local computation.Comment: An extended abstract of this work appears in the 2014 proceedings of
the International Symposium on Distributed Computing (DISC
Some Communication Complexity Results and their Applications
Communication Complexity represents one of the premier techniques for proving lower bounds in theoretical computer science. Lower bounds on communication problems can be leveraged to prove lower bounds in several different areas. In this work, we study three different communication complexity problems. The lower bounds for these problems have applications in circuit complexity, wireless sensor networks, and streaming algorithms. First, we study the multiparty pointer jumping problem. We present the first nontrivial upper bound for this problem. We also provide a suite of strong lower bounds under several restricted classes of protocols. Next, we initiate the study of several non-monotone functions in the distributed functional monitoring setting and provide several lower bounds. In particular, we give a generic adversarial technique and show that when deletions are allowed, no nontrivial protocol is possible. Finally, we study the Gap-Hamming-Distance problem and give tight lower bounds for protocols that use a constant number of messages. As a result, we take a well-known lower bound for one-pass streaming algorithms for a host of problems and extend it so it applies to streaming algorithms that use a constant number of passes
Distributed Computation of Large-scale Graph Problems
Motivated by the increasing need for fast distributed processing of
large-scale graphs such as the Web graph and various social networks, we study
a message-passing distributed computing model for graph processing and present
lower bounds and algorithms for several graph problems. This work is inspired
by recent large-scale graph processing systems (e.g., Pregel and Giraph) which
are designed based on the message-passing model of distributed computing.
Our model consists of a point-to-point communication network of machines
interconnected by bandwidth-restricted links. Communicating data between the
machines is the costly operation (as opposed to local computation). The network
is used to process an arbitrary -node input graph (typically )
that is randomly partitioned among the machines (a common implementation in
many real world systems). Our goal is to study fundamental complexity bounds
for solving graph problems in this model.
We present techniques for obtaining lower bounds on the distributed time
complexity. Our lower bounds develop and use new bounds in random-partition
communication complexity. We first show a lower bound of rounds
for computing a spanning tree (ST) of the input graph. This result also implies
the same bound for other fundamental problems such as computing a minimum
spanning tree (MST). We also show an lower bound for
connectivity, ST verification and other related problems.
We give algorithms for various fundamental graph problems in our model. We
show that problems such as PageRank, MST, connectivity, and graph covering can
be solved in time, whereas for shortest paths, we present
algorithms that run in time (for -factor
approx.) and in time (for -factor approx.)
respectively.Comment: In Proceedings of SODA 201
Lower Bounds on Quantum Query Complexity
Shor's and Grover's famous quantum algorithms for factoring and searching
show that quantum computers can solve certain computational problems
significantly faster than any classical computer. We discuss here what quantum
computers_cannot_ do, and specifically how to prove limits on their
computational power. We cover the main known techniques for proving lower
bounds, and exemplify and compare the methods.Comment: survey, 23 page
Tight Bounds for Set Disjointness in the Message Passing Model
In a multiparty message-passing model of communication, there are
players. Each player has a private input, and they communicate by sending
messages to one another over private channels. While this model has been used
extensively in distributed computing and in multiparty computation, lower
bounds on communication complexity in this model and related models have been
somewhat scarce. In recent work \cite{phillips12,woodruff12,woodruff13}, strong
lower bounds of the form were obtained for several
functions in the message-passing model; however, a lower bound on the classical
Set Disjointness problem remained elusive.
In this paper, we prove tight lower bounds of the form
for the Set Disjointness problem in the message passing model. Our bounds are
obtained by developing information complexity tools in the message-passing
model, and then proving an information complexity lower bound for Set
Disjointness. As a corollary, we show a tight lower bound for the task
allocation problem \cite{DruckerKuhnOshman} via a reduction from Set
Disjointness
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