3,353 research outputs found
Markets are Dead, Long Live Markets
Researchers have long proposed using economic approaches to resource
allocation in computer systems. However, few of these proposals became
operational, let alone commercial. Questions persist about the economic
approach regarding its assumptions, value, applicability, and relevance to
system design. The goal of this paper is to answer these questions. We find
that market-based resource allocation is useful, and more importantly, that
mechanism design and system design should be integrated to produce systems that
are both economically and computationally efficient.Comment: Fix rotation of figure
Amortized Rotation Cost in AVL Trees
An AVL tree is the original type of balanced binary search tree. An insertion
in an -node AVL tree takes at most two rotations, but a deletion in an
-node AVL tree can take . A natural question is whether
deletions can take many rotations not only in the worst case but in the
amortized case as well. A sequence of successive deletions in an -node
tree takes rotations, but what happens when insertions are intermixed
with deletions? Heaupler, Sen, and Tarjan conjectured that alternating
insertions and deletions in an -node AVL tree can cause each deletion to do
rotations, but they provided no construction to justify their
claim. We provide such a construction: we show that, for infinitely many ,
there is a set of {\it expensive} -node AVL trees with the property
that, given any tree in , deleting a certain leaf and then reinserting it
produces a tree in , with the deletion having done
rotations. One can do an arbitrary number of such expensive deletion-insertion
pairs. The difficulty in obtaining such a construction is that in general the
tree produced by an expensive deletion-insertion pair is not the original tree.
Indeed, if the trees in have even height , deletion-insertion
pairs are required to reproduce the original tree
Label optimal regret bounds for online local learning
We resolve an open question from (Christiano, 2014b) posed in COLT'14
regarding the optimal dependency of the regret achievable for online local
learning on the size of the label set. In this framework the algorithm is shown
a pair of items at each step, chosen from a set of items. The learner then
predicts a label for each item, from a label set of size and receives a
real valued payoff. This is a natural framework which captures many interesting
scenarios such as collaborative filtering, online gambling, and online max cut
among others. (Christiano, 2014a) designed an efficient online learning
algorithm for this problem achieving a regret of , where
is the number of rounds. Information theoretically, one can achieve a regret of
. One of the main open questions left in this framework
concerns closing the above gap.
In this work, we provide a complete answer to the question above via two main
results. We show, via a tighter analysis, that the semi-definite programming
based algorithm of (Christiano, 2014a), in fact achieves a regret of
. Second, we show a matching computational lower bound. Namely,
we show that a polynomial time algorithm for online local learning with lower
regret would imply a polynomial time algorithm for the planted clique problem
which is widely believed to be hard. We prove a similar hardness result under a
related conjecture concerning planted dense subgraphs that we put forth. Unlike
planted clique, the planted dense subgraph problem does not have any known
quasi-polynomial time algorithms.
Computational lower bounds for online learning are relatively rare, and we
hope that the ideas developed in this work will lead to lower bounds for other
online learning scenarios as well.Comment: 13 pages; Changes from previous version: small changes to proofs of
Theorems 1 & 2, a small rewrite of introduction as well (this version is the
same as camera-ready copy in COLT '15
Modeling temporal networks using random itineraries
We propose a procedure to generate dynamical networks with bursty, possibly
repetitive and correlated temporal behaviors. Regarding any weighted directed
graph as being composed of the accumulation of paths between its nodes, our
construction uses random walks of variable length to produce time-extended
structures with adjustable features. The procedure is first described in a
general framework. It is then illustrated in a case study inspired by a
transportation system for which the resulting synthetic network is shown to
accurately mimic the empirical phenomenology
- …