Competitive Data-Structure Dynamization

by   Claire Mathieu, et al.

Data-structure dynamization is a general approach for making static data structures dynamic. It is used extensively in geometric settings and in the guise of so-called merge (or compaction) policies in big-data databases such as Google Bigtable and LevelDB (our focus). Previous theoretical work is based on worst-case analyses for uniform inputs – insertions of one item at a time and constant read rate. In practice, merge policies must not only handle batch insertions and varying read/write ratios, they can take advantage of such non-uniformity to reduce cost on a per-input basis. To model this, we initiate the study of data-structure dynamization through the lens of competitive analysis, via two new online set-cover problems. For each, the input is a sequence of disjoint sets of weighted items. The sets are revealed one at a time. The algorithm must respond to each with a set cover that covers all items revealed so far. It obtains the cover incrementally from the previous cover by adding one or more sets and optionally removing existing sets. For each new set the algorithm incurs build cost equal to the weight of the items in the set. In the first problem the objective is to minimize total build cost plus total query cost, where the algorithm incurs a query cost at each time t equal to the current cover size. In the second problem, the objective is to minimize the build cost while keeping the query cost from exceeding k (a given parameter) at any time. We give deterministic online algorithms for both variants, with competitive ratios of Θ(log^* n) and k, respectively. The latter ratio is optimal for the second variant.



There are no comments yet.


page 1

page 2

page 3

page 4


Dynamic Geometric Set Cover, Revisited

Geometric set cover is a classical problem in computational geometry, wh...

Dynamic geometric set cover and hitting set

We investigate dynamic versions of geometric set cover and hitting set w...

The Online Min-Sum Set Cover Problem

We consider the online Min-Sum Set Cover (MSSC), a natural and intriguin...

Faster Approximation Algorithms for Geometric Set Cover

We improve the running times of O(1)-approximation algorithms for the se...

Decremental SSSP in Weighted Digraphs: Faster and Against an Adaptive Adversary

Given a dynamic digraph G = (V,E) undergoing edge deletions and given s∈...

New Results for the k-Secretary Problem

Suppose that n items arrive online in random order and the goal is to se...

Dynamic Membership for Regular Languages

We study the dynamic membership problem for regular languages: fix a lan...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.