Approximation Algorithms for Data Placement Problems

作者：Ivan D. Baev, Rajmohan Rajaraman, Chaitanya Swamy · 发表于：SIAM Journal on Computing · 年份：2008 · DOI：10.1137/080715421 · 被引用次数：222 · 研究领域：Optimization and Search Problems、Facility Location and Emergency Management、Caching and Content Delivery

We develop approximation algorithms for the problem of placing replicated data in arbitrary networks, where the nodes may both issue requests for data objects and have capacity for storing data objects so as to minimize the average data-access cost. We introduce the data placement problem to model this problem. We have a set of caches $\mathcal{F}$, a set of clients $\mathcal{D}$, and a set of data objects $\mathcal{O}$. Each cache i can store at most $u_i$ data objects. Each client $j\in\mathcal{D}$ has demand $d_j$ for a specific data object $o(j)\in\mathcal{O}$ and has to be assigned to a cache that stores that object. Storing an object o in cache i incurs a storage cost of $f_i^o$, and assigning client j to cache i incurs an access cost of $d_jc_{ij}$. The goal is to find a placement of the data objects to caches respecting the capacity constraints, and an assignment of clients to caches so as to minimize the total storage and client access costs. We present a 10-approximation algorithm for this problem. Our algorithm is based on rounding an optimal solution to a natural linear-programming relaxation of the problem. One of the main technical challenges encountered during rounding is to preserve the cache capacities while incurring only a constant-factor increase in the solution cost. We also introduce the connected data placement problem to capture settings where write-requests are also issued for data objects, so that one requires a mechanism to maintain consistency of d...