We study the advice complexity of online buffer management. Advice complexity measures the amount of information about the future that an online algorithm needs to achieve optimality or a good competitive ratio. We study the 2-valued buffer management problem in both preemptive and nonpreemptive models and prove lower and upper bounds on the number of bits required by an optimal online algorith...

We are given an unknown binary matrix, where the entries correspond to preferences of users on items. We want to find at least one 1-entry in each row with a minimum number of queries. The number of queries needed heavily depends on the input matrix and a straightforward competitive analysis yields bad results for any online algorithm. Therefore, we analyze our algorithm against a weaker offlin...

Only recently progress has been made in obtaining o(log(rank))-competitive algorithms for the matroid secretary problem. More precisely, Chakraborty and Lachish (2012) presented a O( √ log(rank))-competitive procedure, and Lachish (2014) later presented a O(log log(rank))competitive algorithm. Both these algorithms and their analyses are very involved, which is also reflected in the extremely h...

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 ...