98 research outputs found
Amortized Dynamic Cell-Probe Lower Bounds from Four-Party Communication
This paper develops a new technique for proving amortized, randomized
cell-probe lower bounds on dynamic data structure problems. We introduce a new
randomized nondeterministic four-party communication model that enables
"accelerated", error-preserving simulations of dynamic data structures.
We use this technique to prove an cell-probe
lower bound for the dynamic 2D weighted orthogonal range counting problem
(2D-ORC) with updates and queries, that holds even
for data structures with success probability. This
result not only proves the highest amortized lower bound to date, but is also
tight in the strongest possible sense, as a matching upper bound can be
obtained by a deterministic data structure with worst-case operational time.
This is the first demonstration of a "sharp threshold" phenomenon for dynamic
data structures.
Our broader motivation is that cell-probe lower bounds for exponentially
small success facilitate reductions from dynamic to static data structures. As
a proof-of-concept, we show that a slightly strengthened version of our lower
bound would imply an lower bound for the
static 3D-ORC problem with space. Such result would give a
near quadratic improvement over the highest known static cell-probe lower
bound, and break the long standing barrier for static data
structures
Pruning based Distance Sketches with Provable Guarantees on Random Graphs
Measuring the distances between vertices on graphs is one of the most
fundamental components in network analysis. Since finding shortest paths
requires traversing the graph, it is challenging to obtain distance information
on large graphs very quickly. In this work, we present a preprocessing
algorithm that is able to create landmark based distance sketches efficiently,
with strong theoretical guarantees. When evaluated on a diverse set of social
and information networks, our algorithm significantly improves over existing
approaches by reducing the number of landmarks stored, preprocessing time, or
stretch of the estimated distances.
On Erd\"{o}s-R\'{e}nyi graphs and random power law graphs with degree
distribution exponent , our algorithm outputs an exact distance
data structure with space between and
depending on the value of , where is the number of vertices. We
complement the algorithm with tight lower bounds for Erdos-Renyi graphs and the
case when is close to two.Comment: Full version for the conference paper to appear in The Web
Conference'1
Randomized vs. Deterministic Separation in Time-Space Tradeoffs of Multi-Output Functions
We prove the first polynomial separation between randomized and deterministic
time-space tradeoffs of multi-output functions. In particular, we present a
total function that on the input of elements in , outputs
elements, such that: (1) There exists a randomized oblivious algorithm with
space , time and one-way access to randomness, that
computes the function with probability ; (2) Any deterministic
oblivious branching program with space and time that computes the
function must satisfy . This implies that
logspace randomized algorithms for multi-output functions cannot be black-box
derandomized without an overhead in time.
Since previously all the polynomial time-space tradeoffs of multi-output
functions are proved via the Borodin-Cook method, which is a probabilistic
method that inherently gives the same lower bound for randomized and
deterministic branching programs, our lower bound proof is intrinsically
different from previous works. We also examine other natural candidates for
proving such separations, and show that any polynomial separation for these
problems would resolve the long-standing open problem of proving
time lower bound for decision problems with
space.Comment: 15 page
Super-Logarithmic Lower Bounds for Dynamic Graph Problems
In this work, we prove a unconditional lower
bound on the maximum of the query time and update time for dynamic data
structures supporting reachability queries in -node directed acyclic graphs
under edge insertions. This is the first super-logarithmic lower bound for any
natural graph problem. In proving the lower bound, we also make novel
contributions to the state-of-the-art data structure lower bound techniques
that we hope may lead to further progress in proving lower bounds
- …