This paper is concerned with the extra-resource analysis of online scheduling algorithms. In particular, it studies how to make use of multiple processors to counteract the lack of future information in online deadlin...
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ISBN:
(纸本)9781581135299
This paper is concerned with the extra-resource analysis of online scheduling algorithms. In particular, it studies how to make use of multiple processors to counteract the lack of future information in online deadline scheduling. Our results extend the previous work that are primarily based on using a faster processor to obtain a performance guarantee. The challenge arises from the fact that jobs are sequential in nature and cannot be executed on more than one processor at the same time. Thus, a faster processor can speed up a job while multiple unit-speed processors cannot help.
Motivated by the availability of real-time data on customer characteristics, we consider the problem of personalizing the assortment of products to each arriving customer. For an arriving customer of type z, the compa...
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ISBN:
(纸本)9781450319621
Motivated by the availability of real-time data on customer characteristics, we consider the problem of personalizing the assortment of products to each arriving customer. For an arriving customer of type z, the company must decide, in real-time, on the assortment of products to offer. Given the offered assortment, the customers make choices on which products to buy, if any, according to a general choice model that is specific to each customer type. Our goal is to develop a revenue-maximizing policy that determines the assortment to offer to each arriving customer, taking into account the customer type and the current *** propose a family of simple and effective algorithms, called Inventory-Balancing, for real-time personalized assortment optimization. Each Inventory-Balancing algorithm is characterized by the penalty function that discounts the marginal revenue of each product, as the inventory level reduces. By adjusting the revenue of each product according to its remaining inventory, the algorithms hedges against the uncertainty in the types of future customers, by reducing the rate at which products with low inventory are offered. Thus, Inventory-Balancing serves as a simple mechanism that coordinates the front-end customer-facing decision with the back-end supply chain *** particular, we prove that Inventory-Balancing algorithms with a strictly concave penalty function always obtain more than 50% of the optimal revenue. We also provide an Inventory-Balancing algorithm that obtains at least 1-1/e ≈ 63% of the benchmark revenue. The 63% ratio is optimal in the sense that no other deterministic or stochastic policies can achieve a higher value. In our numerical experiments, our algorithms perform even better than what is predicted by the worst-case bound, and they obtain revenues that are within 94% of the optimal. Through actual sales data from an online retailer, we also demonstrate that personalization based on each customer's location ca
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))~(1/2))-competitive proc...
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ISBN:
(纸本)9781510813311
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))~(1/2))-competitive procedure, and Lachish (2014) recently presented a O(log log(rank))-competitive algorithm. Both algorithms are involved with complex analyses. Using different tools, we present a considerably simpler O(log log(rank))-competitive algorithm. Our algorithm can be interpreted as a distribution over a simple type of matroid secretary algorithms which are easy to analyze. We are also able to vastly improve on the hidden constant in the competitive ratio.
We study the problem of dynamically allocating T indivisible items to n agents with the restriction that the allocation is fair all the time. Due to the negative results to achieve fairness when allocations are irrevo...
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ISBN:
(纸本)9781450394321
We study the problem of dynamically allocating T indivisible items to n agents with the restriction that the allocation is fair all the time. Due to the negative results to achieve fairness when allocations are irrevocable, we allow adjustments to make fairness attainable with the objective to minimize the number of adjustments. For restricted additive or general identical valuations, we show that envy-freeness up to one item (EF1) can be achieved with no adjustments. For additive valuations, we give an EF1 algorithm that requires O(mT) adjustments, improving the previous result of O(nmT) adjustments, where m is the maximum number of different valuations for items among all *** further impose the contiguity constraint on items such that items are arranged on a line by the order they arrive and require that each agent obtains a consecutive block of items. We present extensive results to achieve either proportionality with an additive approximate factor (PROPa) or EF1, where PROPa is a weaker fairness notion than EF1. In particular, we show that for identical valuations, achieving PROPa requires Θ(nT) adjustments. Moreover, we show that it is hopeless to make any significant improvement for either PROPa or EF1 when valuations are *** results exhibit a large discrepancy between the identical and nonidentical cases in both contiguous and noncontiguous settings. All our positive results are computationally efficient.
Exploration of unknown environments is relevant for many robotics applications, like map building and coverage. Several works in the literature have proposed exploration strategies that drive a mobile robot to greedil...
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ISBN:
(纸本)9781450337717
Exploration of unknown environments is relevant for many robotics applications, like map building and coverage. Several works in the literature have proposed exploration strategies that drive a mobile robot to greedily choose where to go next in order to incrementally map an initially unknown environment. In this paper, we theoretically study the worst and average traveled distance required to explore graph-based environments by some exploration strategies that consider distance and information gain in selecting the next destination location.
A sequence of objects that are characterized by their color has to be processed. Their processing order influences how efficiently they can be processed: Each color change between two consecutive objects produces cost...
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A sequence of objects that are characterized by their color has to be processed. Their processing order influences how efficiently they can be processed: Each color change between two consecutive objects produces costs. A reordering buffer, which is a random access buffer with storage capacity for k objects, can be used to rearrange this sequence online in such a way that the total costs are reduced. This concept is useful for many applications in computer science and *** strategy with the best-known competitive ratio is MAP. An upper bound of O(log k) on the competitive ratio of MAP is known and a nonconstant lower bound on the competitive ratio is not known. Based on theoretical considerations and experimental evaluations, we give strong evidence that the previously used proof techniques are not suitable to show an o(√log k) upper bound on the competitive ratio of MAP. However, we also give some evidence that in fact MAP achieves a competitive ratio of O(1).Further, we evaluate the performance of several strategies on random input sequences experimentally. MAP and its variants RC and RR clearly outperform the other strategies FIFO, LRU, and MCF. In particular, MAP, RC, and RR are the only known strategies whose competitive ratios do not depend on the buffer size. Furthermore, MAP achieves the smallest competitive ratio.
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