We study the online transportation problem. We show that the halfopt-competitive ratio for the greedy algorithm is (min(m; logC)), where m is the number of server sites, and C is the total number of servers. We also present an algorithm Balance that is a modi cation of the greedy algorithm and that has a halfopt-competitive ratio of O(1).

We investigate the online triangle packing problem in which a sequence of equilateral triangles with different sizes appear in an online, sequential manner. The goal is to place these triangles into a minimum number of squares of unit size. We provide upper and lower bounds for the competitive ratio of online algorithms. In particular, we introduce an algorithm which achieves a competitive rati...

We present a lower bound of 1+e ?1=2 1:6065 on the competitive ratio of randomized algorithms for the weighted 2-cache problem, which is a special case of the 2-server problem. This improves the previously best known lower bound of e=(e ? 1) 1:582 for both problems.

We consider the scheduling problem of minimizing the average weighted completion time on identical parallel machines when jobs are arriving over time. For both the preemptive and the nonpreemptive setting, we show that straightforward extensions of Smith’s ratio rule yield smaller competitive ratios compared to the previously best-known deterministic on-line algorithms, which are (4+ ε)-competi...

We give a memoryless scale-invariant randomized algorithm Mix-R for buffer management with bounded delay that is e/(e − 1)-competitive against an adaptive adversary, together with better performance guarantees for many restricted variants, including the s-bounded instances. In particular, Mix-R attains the optimum competitive ratio of 4/3 on 2-bounded instances. Both Mix-R and its analysis are ...

In the rendezvous problem, two robots at unknown locations must successfully meet somewhere in the environment. In the asymmetric formulation, the robots may execute different strategies. We study the symmetric version of the problem, in which they must use the same strategy. We provide a new algorithm for the symmetric rendezvous problem on the line. Our symmetric strategy has a competitive ra...

In this paper we give deterministic competitive k-server algorithms for all k and all metric spaces. This settles the k-server conjecture [MMS] up to the competitive ratio. The best previous result for general metric spaces was a 3-server randomized competitive algorithm [BKT] and a non-constructive proof that a deterministic 3-server competitive algorithm exists [BBKTW]. The competitive ratio ...

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...