Understanding the K-Medians Problem

نویسندگان

  • Christopher Whelan
  • Greg Harrell
چکیده

In this study, the general ideas surrounding the k-medians problem are discussed. This involves a look into what k-medians attempts to solve and how it goes about doing so. We take a look at why k-medians is used as opposed to its k-means counterpart, specifically how its robustness enables it to be far more resistant to outliers. We then discuss the areas of study that are prevalent in the realm of the k-medians problem. Finally, we view an approach to the problem that has decreased its time complexity by instead performing the k-medians algorithm on small coresets representative of the data set.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Greedy Approximation Algorithms for K-Medians by Randomized Rounding

We give an improved approximation algorithm for the general kmedians problem. Given any > 0, the algorithm nds a solution of total distance at most D(1 + ) using at most k ln(n + n= ) medians (a.k.a. sites), provided some solution of total distance D using k medians exists. This improves over the best previous bound (w.r.t. the number of medians) by a factor of (1= ) provided 1= = n. The algori...

متن کامل

Oblivious Medians via Online Bidding

Following Mettu and Plaxton [22, 21], we study oblivious algorithms for the k-medians problem. Such an algorithm produces an incremental sequence of facility sets. We give improved algorithms, including a (24 + )-competitive deterministic polynomial algorithm and a 2e ≈ 5.44-competitive randomized non-polynomial algorithm. Our approach is similar to that of [18], which was done independently. W...

متن کامل

Sub-optimality Approximations

The sub-optimality approximation problem considers an optimization problem O, its optimal solution σ∗, and a variable x with domain {d1, . . . , dm} and returns approximations to O[x← d1], . . . ,O[x← dm], where O[x← d1] denotes the problem O with x assigned to di. The sub-optimality approximation problem is at the core of online stochastic optimization algorithms and it can also be used for so...

متن کامل

ar X iv : c s . D S / 05 04 10 3 v 2 24 J an 2 00 6 Oblivious Medians via Online Bidding ( Extended Abstract )

Following Mettu and Plaxton [22, 21], we study oblivious algorithms for the k-medians problem. Such an algorithm produces an incremental sequence of facility sets. We give improved algorithms, including a (24 + ǫ)-competitive deterministic polynomial algorithm and a 2e ≈ 5.44-competitive, randomized, non-polynomial algorithm. Our approach is similar to that of [18], which was done independently...

متن کامل

A pr 2 00 5 Online Medians via Online Bribery ( Extended Abstract )

Following Mettu and Plaxton [15, 16], we study online algorithms for the k-medians problem. Such an algorithm must produce an incremental sequence F1 ⊆ F2 ⊆ · · · ⊆ Fn ⊆ F of sets of facilities. Mettu and Plaxton show that online metric medians has a (roughly) 40-competitive deterministic polynomial-time algorithm. We give improved algorithms, including a (24 + ǫ)competitive deterministic polyn...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015