In the seat reservation problem, there are k stations, s1 through sk, and one train with n seats departing from the station s1 and arriving at the station sk. Each passenger orders a ticket from station si to station sj (1 ≤ i < j ≤ k) by specifying i and j. The task of an online algorithm is to assign one of n seats to each passenger online, i.e., without knowing future requests. The purpose o...

The paging algorithm Least Recently Used Second-to-Last Request (LRU-2) was proposed for use in database disk buffering and shown experimentally to perform better than Least Recently Used (LRU). We compare LRU-2 and LRU theoretically, using both the standard competitive analysis and the newer relative worst order analysis. The competitive ratio for LRU-2 is shown to be 2k for cache size k, whic...

The k-server problem is one of the most fundamental online problems. The problem is to schedule k mobile servers to visit a sequence of points in a metric space with minimum total mileage. The k-server conjecture of Manasse, McGeogh, and Sleator states that there exists a k-competitive online algorithm. The conjecture has been open for over 15 years. The top candidate online algorithm for settl...

We consider a generalization of the 2-server problem in which servers have diierent costs. We prove that, in uniform spaces, a version of the Work Function Algorithm is 5-competitive, and that no better ratio is possible. We also give a 5-competitive randomized, memoryless algorithm for uniform spaces, and a matching lower bound. For arbitrary metric spaces, in contrast with the non-weighted ca...

We consider the problem of computing energy-efficient broadcast schedules for a speed-controlled broadcast channel, i.e., our goal is to find broadcast schedules that minimze overall energy consumption, where sending at speed s for t time units consumes energy t·sα and transmission speed for each broadcast needs to be fixed when it is started. The main part of the paper is focused on the case t...

We construct an online algorithm for paging that achieves an O(r + log k) competitive ratio when compared to an offline strategy that is allowed the additional ability to “rent” pages at a cost of 1=r. In contrast, the competitive ratio of the Marking algorithm for this scenario is O(r log k). Our algorithm can be thought of in the standard setting as having a “fine-grained” competitive ratio, ...

This paper combines two key ingredients for online algorithms competitive analysis (e.g. the competitive ratio) and advice complexity (e.g. the number of advice bits needed to improve online decisions) in the context of a simple online fair division model where items arrive one by one and are allocated to agents via some mechanism. We consider four such online mechanisms: the popular Rankingmat...

We study the online matching problem when the metric space is a single straight line. For this case, the offline matching problem is trivial but the online problem has been open and the best known competitive ratio was the trivial Θ(n) where n is the number of requests. It was conjectured that the generalized Work Function Algorithm has constant competitive ratio for this problem. We show that ...

In the reordering buffer management problem a sequence of requests arrive online in a finite metric space, and have to be processed by a single server. This server is equipped with a request buffer of size k and can decide at each point in time, which request from its buffer to serve next. Servicing of a request is simply done by moving the server to the location of the request. The goal is to ...

The randomized k-paging algorithm Equitable given by Achlioptas et al. is Hk-competitive and uses O(k 2 log k) memory. This competitive ratio is best possible. The randomized algorithm RMark given by Fiat et al. is (2Hk − 1)-competitive, but only uses O(k) memory. Borodin and El Yaniv [6] list as an open question whether there exists an Hk-competitive randomized algorithm which requires O(k) me...