Better algorithms for unfair metrical task systems and applications

Unfair metrical task systems are a generalization of online metrical task systems. In this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain improved randomized online algorithms for metrical task systems on arbitrary metric spaces.Comment: 20 pages, 1 figur

On-Line Paging against Adversarially Biased Random Inputs

In evaluating an algorithm, worst-case analysis can be overly pessimistic. Average-case analysis can be overly optimistic. An intermediate approach is to show that an algorithm does well on a broad class of input distributions. Koutsoupias and Papadimitriou recently analyzed the least-recently-used (LRU) paging strategy in this manner, analyzing its performance on an input sequence generated by a so-called diffuse adversary -- one that must choose each request probabilitistically so that no page is chosen with probability more than some fixed epsilon>0. They showed that LRU achieves the optimal competitive ratio (for deterministic on-line algorithms), but they didn't determine the actual ratio. In this paper we estimate the optimal ratios within roughly a factor of two for both deterministic strategies (e.g. least-recently-used and first-in-first-out) and randomized strategies. Around the threshold epsilon ~ 1/k (where k is the cache size), the optimal ratios are both Theta(ln k). Below the threshold the ratios tend rapidly to O(1). Above the threshold the ratio is unchanged for randomized strategies but tends rapidly to Theta(k) for deterministic ones. We also give an alternate proof of the optimality of LRU.Comment: Conference version appeared in SODA '98 as "Bounding the Diffuse Adversary

Truly Online Paging with Locality of Reference

The competitive analysis fails to model locality of reference in the online paging problem. To deal with it, Borodin et. al. introduced the access graph model, which attempts to capture the locality of reference. However, the access graph model has a number of troubling aspects. The access graph has to be known in advance to the paging algorithm and the memory required to represent the access graph itself may be very large. In this paper we present truly online strongly competitive paging algorithms in the access graph model that do not have any prior information on the access sequence. We present both deterministic and randomized algorithms. The algorithms need only O(k log n) bits of memory, where k is the number of page slots available and n is the size of the virtual address space. I.e., asymptotically no more memory than needed to store the virtual address translation table. We also observe that our algorithms adapt themselves to temporal changes in the locality of reference. We model temporal changes in the locality of reference by extending the access graph model to the so called extended access graph model, in which many vertices of the graph can correspond to the same virtual page. We define a measure for the rate of change in the locality of reference in G denoted by Delta(G). We then show our algorithms remain strongly competitive as long as Delta(G) >= (1+ epsilon)k, and no truly online algorithm can be strongly competitive on a class of extended access graphs that includes all graphs G with Delta(G) >= k- o(k).Comment: 37 pages. Preliminary version appeared in FOCS '9

THE IMPACT OF THE CAP-AND-TRADE SYSTEM ON SUSTAINABLE DEVELOPMENT IN ROMANIA

The issue of pollution is an important contemporary issue. Within the last 20 years, there have been global studies on how to stop global warming. The European Union is the world leader in concrete measures undertaken in this respect. The introduction of the cap-and-trade system, begun in 2005 with the carbon emission certificate trade mechanism is considered a a modest succes that needs perfecting. The new EU directives of 2009, that come into effect in 2013, test member countries in the area of conventional and renewable energy strategies which have to be adapted to the national environmental protection strategies.market failure, cap-and-trade, emission certificates, carbon market

Oblivious Transfer based on Key Exchange

Key-exchange protocols have been overlooked as a possible means for implementing oblivious transfer (OT). In this paper we present a protocol for mutual exchange of secrets, 1-out-of-2 OT and coin flipping similar to Diffie-Hellman protocol using the idea of obliviously exchanging encryption keys. Since, Diffie-Hellman scheme is widely used, our protocol may provide a useful alternative to the conventional methods for implementation of oblivious transfer and a useful primitive in building larger cryptographic schemes.Comment: 10 page

Makespan Minimization via Posted Prices

We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: the ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm. We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms