You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We explore a real-time Twitter search application where tweets are arriving at a rate of several thousands per second. Real-time search demands that they be indexed and searchable immediately, which leads to a number of implementation challenges. In this paper, we focus on one aspect: dynamic postings allocation policies for index structures that are completely held in main memory. The core issue can be characterized as a "Goldilocks Problem". Because memory remains today a scare resource, an allocation policy that is too aggressive leads to inefficient utilization, while a policy that is too conservative is slow and leads to fragmented postings lists. We present a dynamic postings allocation policy that allocates memory in increasingly-larger "slices" from a small number of large, fixed pools of memory. Through analytical models and experiments, we explore different settings that balance time (query evaluation speed) and space (memory utilization).

Cited Abstract(s):
[1]: Bigtable is a distributed storage system for managing structured data that is designed to scale to a very large size: petabytes of data across thousands of commodity servers. Many projects at Google store data in Bigtable, including web indexing, Google Earth, and Google Finance. These applications place very different demands on Bigtable, both in terms of data size (from URLs to web pages to satellite imagery) and latency requirements (from backend bulk processing to real-time data serving). Despite these varied demands, Bigtable has successfully provided a flexible, high-performance solution for all of these Google products. In this paper we describe the simple data model provided by Bigtable, which gives clients dynamic control over data layout and format, and we describe the design and implementation of Bigtable.

[2]: Updating an index of the web as documents are crawled requires continuously transforming a large repository of existing documents as new documents arrive. This task is one example of a class of data processing tasks that transform a large repository of data via small, independent mutations. These tasks lie in a gap between the capabilities of existing infrastructure. Databases do not meet the storage or throughput requirements of these tasks: Google's indexing system stores tens of petabytes of data and processes billions of updates per day on thousands of machines. MapReduce and other batch-processing systems cannot process small updates individually as they rely on creating large batches for efficiency. We have built Percolator, a system for incrementally processing updates to a large data set, and deployed it to create the Google web search index. By replacing a batch-based indexing system with an indexing system based on incremental processing using Percolator, we process the same number of documents per day, while reducing the average age of documents in Google search results by 50 .
Another interesting point in the design space is represented by Google's Percolator architecture [2] , which is built on top of Bigtable [1] ---a distributed, multi-dimensional sparse sorted map based log-structured merge trees. Percolator supports incremental data processing through observers , similar to database triggers, which provide cross-row transactions, whereas Bigtable only supports single-row transactions. This architecture represents a very different design from our system, which makes a fair comparison difficult. The performance figures reported by the authors suggest that Earlybird is much faster in indexing, but in fairness, this is an apples-to-oranges comparison. Percolator was designed to encompass the entire webpage ingestion pipeline, handling not only indexing but other aspects of document processing as well---whereas Earlybird is highly specialized for building in-memory inverted indexes.