A deterministic truthful PTAS for scheduling related machines

Scheduling on related machines ($Q||C_{\max}$) is one of the most important problems in the field of Algorithmic Mechanism Design. Each machine is controlled by a selfish agent and her valuation can be expressed via a single parameter, her {\em speed}. In contrast to other similar problems, Archer and Tardos \cite{AT01} showed that an algorithm that minimizes the makespan can be truthfully implemented, although in exponential time. On the other hand, if we leave out the game-theoretic issues, the complexity of the problem has been completely settled -- the problem is strongly NP-hard, while there exists a PTAS \cite{HS88,ES04}. This problem is the most well studied in single-parameter algorithmic mechanism design. It gives an excellent ground to explore the boundary between truthfulness and efficient computation. Since the work of Archer and Tardos, quite a lot of deterministic and randomized mechanisms have been suggested. Recently, a breakthrough result \cite{DDDR08} showed that a randomized truthful PTAS exists. On the other hand, for the deterministic case, the best known approximation factor is 2.8 \cite{Kov05,Kov07}. It has been a major open question whether there exists a deterministic truthful PTAS, or whether truthfulness has an essential, negative impact on the computational complexity of the problem. In this paper we give a definitive answer to this important question by providing a truthful {\em deterministic} PTAS

Designing Networks with Good Equilibria under Uncertainty

We consider the problem of designing network cost-sharing protocols with good equilibria under uncertainty. The underlying game is a multicast game in a rooted undirected graph with nonnegative edge costs. A set of k terminal vertices or players need to establish connectivity with the root. The social optimum is the Minimum Steiner Tree. We are interested in situations where the designer has incomplete information about the input. We propose two different models, the adversarial and the stochastic. In both models, the designer has prior knowledge of the underlying metric but the requested subset of the players is not known and is activated either in an adversarial manner (adversarial model) or is drawn from a known probability distribution (stochastic model). In the adversarial model, the designer's goal is to choose a single, universal protocol that has low Price of Anarchy (PoA) for all possible requested subsets of players. The main question we address is: to what extent can prior knowledge of the underlying metric help in the design? We first demonstrate that there exist graphs (outerplanar) where knowledge of the underlying metric can dramatically improve the performance of good network design. Then, in our main technical result, we show that there exist graph metrics, for which knowing the underlying metric does not help and any universal protocol has PoA of $\Omega(\log k)$, which is tight. We attack this problem by developing new techniques that employ powerful tools from extremal combinatorics, and more specifically Ramsey Theory in high dimensional hypercubes. Then we switch to the stochastic model, where each player is independently activated. We show that there exists a randomized ordered protocol that achieves constant PoA. By using standard derandomization techniques, we produce a deterministic ordered protocol with constant PoA.Comment: This version has additional results about stochastic inpu

On the Efficiency of the Proportional Allocation Mechanism for Divisible Resources

We study the efficiency of the proportional allocation mechanism, that is widely used to allocate divisible resources. Each agent submits a bid for each divisible resource and receives a fraction proportional to her bids. We quantify the inefficiency of Nash equilibria by studying the Price of Anarchy (PoA) of the induced game under complete and incomplete information. When agents' valuations are concave, we show that the Bayesian Nash equilibria can be arbitrarily inefficient, in contrast to the well-known 4/3 bound for pure equilibria. Next, we upper bound the PoA over Bayesian equilibria by 2 when agents' valuations are subadditive, generalizing and strengthening previous bounds on lattice submodular valuations. Furthermore, we show that this bound is tight and cannot be improved by any simple or scale-free mechanism. Then we switch to settings with budget constraints, and we show an improved upper bound on the PoA over coarse-correlated equilibria. Finally, we prove that the PoA is exactly 2 for pure equilibria in the polyhedral environment.Comment: To appear in SAGT 201

Tight Bounds for the Price of Anarchy of Simultaneous First Price Auctions

We study the Price of Anarchy of simultaneous first-price auctions for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian Price of Anarchy of these auctions are e/(e-1) [Syrgkanis and Tardos 2013] and 2 [Feldman et al. 2013], respectively. We provide matching lower bounds for both cases even for the case of full information and for mixed Nash equilibria via an explicit construction. We present an alternative proof of the upper bound of e/(e-1) for first-price auctions with fractionally subadditive valuations which reveals the worst-case price distribution, that is used as a building block for the matching lower bound construction. We generalize our results to a general class of item bidding auctions that we call bid-dependent auctions (including first-price auctions and all-pay auctions) where the winner is always the highest bidder and each bidder's payment depends only on his own bid. Finally, we apply our techniques to discriminatory price multi-unit auctions. We complement the results of [de Keijzer et al. 2013] for the case of subadditive valuations, by providing a matching lower bound of 2. For the case of submodular valuations, we provide a lower bound of 1.109. For the same class of valuations, we were able to reproduce the upper bound of e/(e-1) using our non-smooth approach.Comment: 37 pages, 5 figures, ACM Transactions on Economics and Computatio

Groundwater investigation in Paphos region

Cyprus is a semi-arid island. Its water resources rely on winter rainfall which supply the impounding reservoirs constructed on the dry river courses and replenish the groundwater resources within the river gravels or the plain aquifers. water requirements for domestic use and irrigation have been increasing considerably for the last ten years. The potential of the conventional water resources have been developed according to techno-economic factors. Also, the unconventional sources (treated domestic effluents and desalinating sea water) are receiving particular attention to support water requirements throughout the island. The current study deals partly with the calcarenite aquifer of the Paphos Coastal Plain. It has been investigated whether this resource is offered for an integrated exploitation program. In addition the domestic effluent of the Paphos urban zone is considered as a promising resource for providing reliable and continuous quantities for irrigation use after treatment. [Continues.

Characterization of the Ezousas aquifer in south-west Cyprus for the storage and recovery of treated sewage effluent

This thesis reports on research from a full-scale demonstration project to recharge a depleted aquifer with treated sewage effluent from the Paphos (Cyprus) wastewater treatment plant. The project artificially recharged the Ezousas river basin, located in the south-western coastal plain of Cyprus, with tertiary treated, disinfected effluent through a network of artificial infiltration ponds. The aims of the research were to determine the capacity of the aquifer to provide a suitable buffer for the flow from the wastewater without flooding and to measure the changes in reclaimed water quality. The aquifer hydraulics and treatment capacity, including recharge basins, were analysed using field and laboratory measurements. A geological field survey and modelling was used to assess, both by practice and theory the effectiveness of the Ezousas river aquifer for storage and recovery of the reclaimed water. The aquifer was found to be mainly composed of alluvium with typical hydraulic characteristics. The average porosity was 20% and hydraulic conductivity around 90 m/day, it was concluded the aquifer would be able to accept all the annual output of the treatment plant which was 5 Mm3 /a. The recharge network consisted of five groups of infiltration basins arranged on both banks of the River Ezousas about 2km upstream of the wastewater treatment plant. Each infiltration basin contained two, four or six recharge ponds, each basin was 2,000m2 in area with a depth of 1.5 m. A recharge pattern consisting of alternating weeks of wet-fill and drying cycles was found necessary to maintain the unsaturated zone below the ponds in order to maximise the amount of water that could be recharged whilst optimising water quality. The hydraulic impact of the artificial recharge and extraction from the field measurements of borehole water levels indicated recharged water down to 15m below the surface. Tracer tests on the groundwater flow, capture zone, residence times and mass balances of recharged and native waters gave widely varying residence times between 30 days and 5 years, these were attributed to the complex flow patterns found. Recharged water was sampled using a series of extraction wells located along the downstream river basin, starting at the infiltration ponds and then at stages downstream. Eight production and monitoring wells were tested including control samples up-gradient (upstream) from the ponds, to about 7km down-gradient (downstream). Water quality was analyzed for the standard wastewater constituents including indicator organisms, organic matter, nutrients N and P and the metals. It was one of the recommendations of the thesis however that attention also be paid to the persistent organics, including the pesticides, biocides, plasticizers and pharma residues. The chemical data was used to build and validate a solute transport model of the ponds and surrounding area to predict the transport and fate of priority contaminants. In this way, the geo-chemical potential for the retardation, attenuation and chemical or biochemical degradation processes taking place in the unsaturated and saturated zone were assessed. From the results it was concluded that for most analytes, which included metals, nitrate and common salts, the main processes were mixing and dilution by the native ground water. The extracted water was then a mix of waters according to the different residence times and flow of natural groundwater, giving a stable water quality for irrigation. A third reaction involving cation exchange with the local geology was however identified which reduced the concentrations of copper and phosphate beyond what was expected from just mixing. It was also concluded that denitrification did not occur because of a combination of the high quality of the effluent, the operational cycling of the ponds and the high porosity of the vadose zone. Previous work has found denitrification if the recycled water still contains organic matter, further work was recommended to determine the critical organic concentrations. The renovated water from the Ezousas wastewater reuse Project was able to meet the health and agronomic requirements for unrestricted irrigation. The risk of flooding with sewage effluent resulting from hydraulic mounding was also investigated to define the growth and decay of the mound. It was possible to report that after more than fifteen years of operation and a total infiltration of 40Mm3, there have been no signs of reduced hydraulic capacity or water quality