Multi-unit auctions with unknown supply

In this paper, the authors consider an on-line scheduling problem of m (m ≥ 3) identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive ratio \(4 - \tfrac{1} {m} \). In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is \(\tfrac{{10}} {3} \).

We extend the Mobile Server problem introduced in Feldkord and Meyer auf der Heide (TOPC 6(3), 14:1–14:17 2019) to a model where k identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. To reduce communication costs, the positions of the servers can be adapted by a limited distance ms per round for each server. The costs are measured similarly to the classical Page Migration problem: i.e., answering a request induces costs proportional to the distance to the nearest server, and moving a server induces costs proportional to the distance multiplied with a weight D. We show that, in our model, no online algorithm can have a constant competitive ratio: i.e., one which is independent of the input length n, even if an augmented moving distance of (1 + δ)ms is allowed for the online algorithm. Therefore we investigate a restriction of the power of the adversary dictating the sequence of requests: We demand locality of requests: i.e., that consecutive requests come from points in the Euclidean space with distance bounded by some constant mc. We show constant lower bounds on the competitiveness in this setting (independent of n, but dependent on k, ms and mc). On the positive side, we present a deterministic online algorithm with bounded competitiveness when an augmented moving distance and locality of requests is assumed. Our algorithm simulates any given algorithm for the classical k-Page Migration problem as guidance for its servers and extends it by a greedy move of one server in every round. The resulting competitive ratio is polynomial in the number of servers k, the ratio between mc and ms, the inverse of the augmentation factor 1/δ and the competitive ratio of the simulated k-Page Migration algorithm. We also show how to directly adapt the Double Coverage algorithm (Chrobak et al. SIAM J. Discrete Math. 4(2), 172–181 11) for the k-Server problem to receive an algorithm with improved competitiveness on the line.

Constructing a tree spanning a given subset of vertices of a graph is a generic problem that has been extensively studied (for example the classical Steiner tree is one of them). In this paper, we propose to take into account a problem that has not been often studied: the dynamic part, in which new vertices must be inserted in a given tree. We propose to do these insertions with respect of structural constraints that we describe and to capture the efficiency of algorithms by a particular type of competitive ratios. The parameter to optimize in our study is related to distances between the connected vertices. Our main results are the following. We propose a method, called median-addition. We prove that its competitive ratio is non constant but optimal. This result is proved under the hypothesis that the algorithm does not know the sequence of added vertices (called unknown-future or online model). This method can be used to design communication structures for applications like video-conference in networks for example. In another part of the paper, we prove the surprising following result: even if the algorithm knows the sequence of additions of new vertices (hence everything is known in advance), no algorithm can have a constant competitive ratio.

Quantifying the inefficiency of multi-unit auctions for normal goods

An Optimal ICO Mechanism

In this paper we study the problem of on-line allocation of routes to virtual circuits (both point-to-point and multicast ) where the goal is to route all requests while minimizing the required bandwidth. We concentrate on the case of Permanent virtual circuits (i.e., once a circuit is established it exists forever), and describe an algorithm that achieves on O (log n ) competitive ratio with respect to maximum congestin, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O (log n ) factor. We also show that this result is tight, that is, for any on-line algorithm there exists a scenario in which Ω(log n ) increase in bandwidth is necessary in directed networks. We view virtual circuit routing as a generalization of an on-line load balancing problem, defined as follows: jobs arrive on line and each job must be assigned to one of the machines immediately upon arrival. Assigning a job to a machine increases the machine's load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load. For the related machines case, we describe the first algorithm that achieves constant competitive ratio. for the unrelated case (with n machines), we describe a new method that yields O (log n )-competitive algorithm. This stands in contrast to the natural greed approach, whose competitive ratio is exactly n .

Procurement Efficiency in Public Procurement Auctions: Analysis of Different Types of Products

Maintaining data communication in the presence of jammer nodes is an important feature required in several modern wireless networks. In this article, we analyze a three node system, where a legitimate link between the transmitter and the receiver is adversarially affected by independent Gaussian noise injected by a jammer. The transmitter is battery powered, and has data arriving as packets. All the data need to be delivered to the receiver before a common deadline. The transmitter's goal is to accomplish this task using as minimum an energy as possible, while the jammer's objective is the opposite, viz. increase the transmitter's energy as much as possible by strategically injecting noise. We consider a jammer node which relies on dynamic energy harvesting sources to power its hardware. The adversarial interactions are modeled by posing a min-max game between the transmitter and the jammer. Solving this, we derive the equilibrium scheduling policies of the transmitter and the jammer for the offline model, and present an iterative algorithm to compute these policies. Competitive online scheduling policies are then proposed, whose competitive ratio is bounded using ideas from the offline policies derived earlier. A constant competitive ratio is shown when the last data packet does not arrive too early, and a significant fraction of the jamming energy is harvested before this arrival.

In this paper, we consider the on-line single machine scheduling problem with release dates and submodular rejection penalties. We are given a single machine and a sequence of jobs that arrive on-line and must be immediately and irrevocably either assigned on the machine or rejected. The objective is to minimize the sum of the makespan of the accepted jobs and the penalty of the rejected jobs which is determined by a submodular function. We prove that there is no on-line algorithm with a constant competitive ratio if the penalty submodular function is nonmonotone. When the penalty submodular function is monotone, we present an on-line algorithm with a competitive ratio 3.KeywordsOn-line schedulingSubmodular penaltiesOn-line algorithmCompetitive ratio

We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. Intuitively, our direct product theorems say that if b bits of advice are needed to ensure a cost of at most t for some problem, then r*b bits of advice are needed to ensure a total cost of at most r*t when solving r independent instances of the problem. Using our direct product theorems, we are able to translate decades of research on randomized online algorithms to the advice complexity model. Doing so improves significantly on the previous best advice complexity lower bounds for many online problems, or provides the first known lower bounds. For example, we show that - A paging algorithm needs Omega(n) bits of advice to achieve a competitive ratio better than H_k = Omega(log k), where k is the cache size. Previously, it was only known that Omega(n) bits of advice were necessary to achieve a constant competitive ratio smaller than 5/4. - Every O(n^{1-epsilon})-competitive vertex coloring algorithm must use Omega(n log n) bits of advice. Previously, it was only known that Omega(n log n) bits of advice were necessary to be optimal. For certain online problems, including the MTS, k-server, metric matching, paging, list update, and dynamic binary search tree problem, we prove that randomization and sublinear advice are equally powerful (if the underlying metric space or node set is finite). This means that several long-standing open questions regarding randomized online algorithms can be equivalently stated as questions regarding online algorithms with sublinear advice. For example, we show that there exists a deterministic O(log k)-competitive k-server algorithm with sublinear advice if and only if there exists a randomized O(log k)-competitive k-server algorithm without advice. Technically, our main direct product theorem is obtained by extending an information theoretical lower bound technique due to Emek, Fraigniaud, Korman, and Rosen [ICALP'09].

A sequence of objects which 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 economics. The 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 non-constant lower bound on the competitive ratio is not known [2]. Based on theoretical considerations and experimental evaluations, we give strong evidence that the previously used proof techniques are not suitable to show an $o(\sqrt{\log k})$ 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 constant competitive ratio.

We develop a new approach for online network design and obtain improved competitive ratios for several problems. Our approach gives natural deterministic algorithms and simple analyses. At the heart of our work is a novel application of embeddings into hierarchically well-separated trees (HSTs) to the analysis of online network design algorithms --- we charge the cost of the algorithm to the cost of the optimal solution on any HST embedding of the terminals. This analysis technique is widely applicable to many problems and gives a unified framework for online network design. In a sense, our work brings together two of the main approaches to online network design. The first uses greedy-like algorithms and analyzes them using dual-fitting. The second uses tree embeddings and results in randomized $O(\log n)$-competitive algorithms, where $n$ is the total number of vertices in the graph. Our approach uses deterministic greedy-like algorithms but analyzes them via HST embeddings of the terminals. Our proofs are simpler as we do not need to carefully construct dual solutions and we get $O(\log k)$ competitive ratios, where $k$ is the number of terminals. In this paper, we apply our approach to obtain deterministic $O(\log k)$-competitive online algorithms for the following problems. - Steiner network with edge duplication. Previously, only a randomized $O(\log n)$-competitive algorithm was known. - Rent-or-buy. Previously, only deterministic $O(\log^2 k)$-competitive and randomized $O(\log k)$-competitive algorithms by Awerbuch, Azar and Bartal (2004) were known. - Connected facility location. Previously, only a randomized $O(\log^2 k)$-competitive algorithm by San Felice, Williamson and Lee (2014) was known. - Prize-collecting Steiner forest. We match the competitive ratio first achieved by Qian and Williamson (2011) and give a simpler analysis.

Online auction marketplaces such as eBay are susceptible to adverse selection. Due to information asymmetry between buyers and sellers, buyers of luxury goods from online auctions face uncertainty, especially because they are unable to determine the authenticity of goods sold in these marketplaces. Using data from completed auctions on eBay, this study confirms that adverse selection exists for luxury goods in online auctions. Institutions, such as authenticity money-back guarantee, do not effectively mitigate the adverse selection problem. The results also show that sellers tend to set up a reserve price to protect themselves from adverse selection when they choose a low starting bid. However, reserve price auctions for luxury goods result in a lower closing price and such a protection does not economically benefit the sellers. Alternatively, when sellers choose a high starting bid to lower the risk of adverse selection, they tend to offer a buy-it-now price, and the buyout option positively affects the closing price. The implications of our findings for research and practice are also discussed.

Although data has become an important kind of commercial goods, there are few appropriate online platforms to facilitate the trading of mobile crowd-sensed data so far. In this paper, we present the first architecture of mobile crowd-sensed data market, and conduct an in-depth study of the design problem of online data pricing and reward sharing. To build a practical mobile crowd-sensed data market, we have to consider four major design challenges: data uncertainty, economic-robustness (arbitrage-freeness in particular), profit maximization, and fair reward sharing. By jointly considering the design challenges, we propose an online query-bAsed cRowd-sensEd daTa pricing mEchanism, namely ARETE-PR, to determine the trading price of crowd-sensed data. Our theoretical analysis shows that ARETE-PR guarantees both arbitrage-freeness and a constant competitive ratio in terms of profit maximization. Based on some fairness criterions, we further design a reward sharing scheme, namely ARETE-SH, which is closely coupled with ARETE-PR, to incentivize data providers to contribute data. We have evaluated ARETE on a real-world sensory data set collected by Intel Berkeley lab. Evaluation results show that ARETE-PR outperforms the state-of-the-art pricing mechanisms, and achieves around 90 percent of the optimal revenue. ARETE-SH distributes the reward among data providers in a fair way.

Mobile crowdsensing has become increasingly popular due to its ability to collect a massive amount of data with the help ofmany individual smartphone users. Due to the rationality of smartphone users, designing an incentive mechanism to compensate the participants for their resources consumption is critical in attracting more participation. Offline incentive mechanism design has been widely studied in various crowdsensing applications, whereas the online scenario, is much more challenging due to the unavailability of future information when the platform makes user selection decisions. In this paper, we investigate the problem of online crowdsensing by considering a critical property that the values of users contributions decrease as time goes by. The time-discounting property is common in inter-temporal choice scenarios but has not been carefully addressed in mechanism design perspective. To handle this problem, we propose a new method to select users based on a time-related threshold, and present a strategyproof framework where participants prefer to submit their true types, instead of manipulating the market by misreporting their private information. We prove that our mechanisms can achieve computational efficiency, budget feasibility, strategy-proofness, and a constant competitive ratio.