Winner Determination Algorithm Research Articles

Winner Determination Algorithms for Graph Games with Matching Structures

Winner Determination Algorithms for Graph Games with Matching Structures

Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results


 
 
 A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced by Demange (1982), and subsequently Trick (1989b) described an efficient algorithm for deciding if a given profile is single-peaked on a tree. We study the complexity of multiwinner elections under several variants of the Chamberlin–Courant rule for preferences single-peaked on trees. We show that in this setting the egalitarian version of this rule admits a polynomial-time winner determination algorithm. For the utilitarian version, we prove that winner determination remains NP-hard for the Borda scoring function; indeed, this hardness results extends to a large family of scoring functions. However, a winning committee can be found in polynomial time if either the number of leaves or the number of internal vertices of the underlying tree is bounded by a constant. To benefit from these positive results, we need a procedure that can determine whether a given profile is single-peaked on a tree that has additional desirable properties (such as, e.g., a small number of leaves). To address this challenge, we develop a structural approach that enables us to compactly represent all trees with respect to which a given profile is single-peaked. We show how to use this representation to efficiently find the best tree for a given profile for use with our winner determination algorithms: Given a profile, we can efficiently find a tree with the minimum number of leaves, or a tree with the minimum number of internal vertices among trees on which the profile is single-peaked. We then explore the power and limitations of this framework: we develop polynomial-time algorithms to find trees with the smallest maximum degree, diameter, or pathwidth, but show that it is NP-hard to check whether a given profile is single-peaked on a tree that is isomorphic to a given tree, or on a regular tree.
 
 

Design, modeling, and analysis of online combinatorial double auction for mobile cloud computing markets

SummaryWith the burgeoning of cloud service companies, cloud computing is becoming an efficient means of providing computing resources. Amazon EC2, Rackspace, Google App, and Microsoft Azure are attracting more and more users over the Internet these years. However, in mobile cloud computing (MCC), traditional cloud pricing models can no longer support the above popular applications, because user behaviors are dynamic and time sensitive. As an MCC application is the combination of communication services (eg, wireless access services) and computation services (eg, cloud services), it lacks new auctions for capturing the feature of MCC markets based on the communication and computation cooperation (3C).In this paper, we design an efficient double‐sided combinatorial auction model in the context of 3C‐based MCC to mitigate this problem. We first propose the framework of online combinatorial double auctions to model mobile cloud computing market. On this base, we give four principles of design requirements, which can make the scheme more efficient and practical, and then we design a new winner determination algorithm that shows how the auction mechanism decides commodity allocation and transaction prices. At last, we conduct a series of experiments to deep analyze the property of our mechanism. The experiment results indicate that the proposed online auction mechanism obtains comparable allocation efficiency to the social optimal solution.

Physical Machine Resource Management in Clouds: A Mechanism Design Approach

We address the problem of physical machine resource management in clouds considering multiple types of physical machines and resources. We formulate this problem in an auction-based setting and design optimal and approximate strategy-proof mechanisms that solve it. Our proposed mechanisms consist of a winner determination algorithm that selects the users, provisions the virtual machines (VMs) to physical machines (PMs), and allocates them to the selected users; and a payment function that determines the amount that each selected user needs to pay to the cloud provider. We prove that our proposed approximate winner determination algorithm satisfies the loser-independent property, making the approximate mechanism robust against strategic users who try to manipulate the system by changing other users’ allocations. We show that our proposed mechanisms are strategy-proof, that is, the users do not have incentives to lie about their requested bundles of VM instances and their valuations. In addition, our proposed mechanisms are in alignment with green cloud computing strategies in which physical machines can be powered on or off to save energy. Our theoretical analysis shows that the proposed approximation mechanism has an approximation ratio of 3. We perform extensive experiments in order to investigate the performance of our proposed approximation mechanism compared to that of the optimal mechanism.

SAT-Based Strategy Extraction in Reachability Games

Reachability games are a useful formalism for the synthesis of reactive systems. Solving a reachability game involves (1) determining the winning player and (2) computing a winning strategy that determines the winning player's action in each state of the game. Recently, a new family of game solvers has been proposed, which rely on counterexample-guided search to compute winning sequences of actions represented as an abstract game tree. While these solvers have demonstrated promising performance in solving the winning determination problem, they currently do not support strategy extraction. We present the first strategy extraction algorithm for abstract game tree-based game solvers. Our algorithm performs SAT encoding of the game abstraction produced by the winner determination algorithm and uses interpolation to compute the strategy. Our experimental results show that our approach performs well on a number of software synthesis benchmarks.

Winner Determination Algorithms for Combinatorial Auctions with Sub-cardinality Constraints

We examine the winner determination problem for combinatorial auctions with sub-cardinality constraints (WDP-SC). In this type of auction, bidders submit bids for packages of items of interest together with a specific number of items they want. All items in a package are equally acceptable, but each bidder wants only the specified number of items in their package and not necessarily all. This type of auction is particularly relevant in cases where bidders are interested in items in close proximity to one another and view items as largely substitutable. We show that WDP-SC is NP-hard. We then develop an integer programming (IP) formulation and two approximation algorithms for solving WDP-SC: one based on simulated annealing (SA) and one based on the Metaheuristic for Randomized Priority Search (Meta-RaPS). We assess the performance of these three methods through computational tests performed on sets of large benchmark problems (ranging from 1000 to 10,000 bids) generated from four different distributions: two developed specifically to simulate proximity concerns, and two others previously used in the literature. IP produced the best solutions for 1000-bid problems, but in many cases SA and Meta-RaPS produced better solutions than IP on larger problems. Both IP and Meta-RaPS appear to be robust solution methods for this problem and consistently produced high-quality solutions across all problem sizes and distributions.

Combinatorial auction based spectrum allocation under heterogeneous supply and demand

In this paper, we apply the combinatorial auction scheme to solve the spectrum allocation problem under heterogeneous supply and demand in cognitive radio networks. The heterogeneity of spectrum is embodied via exploiting multiple attributes, based on which a valuation function is devised to evaluate the preference of an SU over a spectrum band. We first propose an auction scheme consisting of a greedy-like winner determination algorithm and a critical value based discriminatory pricing policy. We then extend the proposed auction scheme to a more challenging scenario by considering spectrum sharing among SUs. Theoretical analysis demonstrates that our auction schemes achieve individual rational, budget balance, value-truthfulness of SUs, and weak value-truthfulness of PUs. Our simulation results verify the advantage of combinatorial auction, the functionality of spectrum sharing and the economic robustness of our auction schemes.

Double Combinatorial Auction based Resource Allocation in Cloud Computing by Combinational using of ICA and Genetic Algorithms

Computational resources have become cheaper, more powerful and accessible than ever with the development of processing and strong technology and internet success. This technology has realized a new computing model called cloud computing in which resources are provided as a service to users and users can rent them or rent of them based on their demands. One of the problems with cloud computing is related to optimizing the allocated resources. Resource allocation is done with the aim of minimizing costs, times and due to the uniqueness of model. In this paper, one double combinatorial auction based resource allocation approach has been proposed. The purpose of this study is to allocate economic resources in a way that lead to increase social welfare. Resource allocation in double combinatorial auction includes two phases. These two phases are winner determination and resource allocation. The proposed approach implement ICA for winner determination and genetic algorithm for resource allocation and payment Schemes .we name this algorithm as IG. The experimental results showed that our proposed algorithm improves the profits of providers and users and works well than other algorithms in the term of increasing providers’ profit. General Terms Cloud computing, resource allocation

A Winner Determination Algorithm for Combinatorial Auctions Based on Hybrid Artificial Fish Swarm Algorithm

Abstract The problem of winner determination in combinatorial auctions is a hotspot electronic business, and a NP hard problem. A Hybrid Artificial Fish Swarm Algorithm(HAFSA), which is combined with First Suite Heuristic Algorithm (FSHA) and Artificial Fish Swarm Algorithm (AFSA), is proposed to solve the problem after probing it base on the theories of AFSA. Experiment results show that the HAFSA is a rapidly and efficient algorithm for The problem of winner determining. Compared with Ant colony Optimization Algorithm, it has a good performance with broad and prosperous application.

Constraint-Based Winner Determination for Auction-Based Scheduling

This paper presents a formulation and an algorithm for the winner determination problem in auction-based scheduling. Without imposing a time line discretization, the proposed approach allows bidders to bid for the processing of a set of jobs using a requirement-based bidding language, which naturally represents scheduling constraints. The proposed winner determination algorithm uses a depth first branch and bound search. The search branches on bids, and a constraint-directed scheduling procedure is used at each node to verify the feasibility of the temporary schedule. Experiments show that the proposed algorithm is on average more than an order of magnitude faster than a commercial optimization package, CPLEX 10.0.

On the Fastest Vickrey Algorithm

We investigate the algorithmic performance of Vickrey-Clarke-Groves mechanisms in the single item case. We provide a formal definition of a Vickrey algorithm for this framework, and give a number of examples of Vickrey algorithms. We consider three performance criteria, one corresponding to a Pareto criterion, one to worst-case analysis, and one related to first-order stochastic dominance. We show that Pareto best Vickrey algorithms do not exist and that worst-case analysis is of no use in discriminating between Vickrey algorithms. For the case of two bidders, we show that the bisection auction stochastically dominates all Vickrey algorithms. We extend our analysis to the study of weak Vickrey algorithms and winner determination algorithms. For the case of two bidders, we show that the One-Search algorithm stochastically dominates all column monotonic weak Vickrey algorithms and that a suitably adjusted version of the bisection algorithm, the WD bisection algorithm, stochastically dominates all winner determination algorithms. The WD bisection algorithm Pareto dominates all column monotonic winner determination algorithms in the n bidder case.

Benders-based winner determination algorithm for volume discount procurement auctions

This paper considers an industrial procurement of large volume of a single good, such as a raw material or a subcomponent. The procurement is implemented using volume discount auctions, in which the bids are nonconvex piecewise linear cost functions. The winner determination problem faced by the buyer is an NP-hard nonlinear knapsack problem. We propose a mixed integer linear formulation for the problem which has the following primal structure: if the integer variables are fixed at some feasible values, then solving the remaining linear variables is a continuous knapsack problem. Exploiting this feature, Benders' decomposition algorithm is developed and various techniques are proposed to accelerate the convergence of the algorithm. Experimental results for the random test data show the efficacy of the accelerating techniques.

A test suite for the evaluation of mixed multi-unit combinatorial auctions

Mixed Multi-Unit Combinatorial Auctions extend and generalize all the preceding types of combinatorial auctions. In this paper, we try to make headway on the practical application of MMUCAs by: (1) providing an algorithm to generate artificial data that is representative of the sort of scenarios a winner determination algorithm is likely to encounter; and (2) subsequently assessing the performance of an Integer Programming implementation of MMUCA in CPLEX.

A New Pricing Model for Next Generation Spectrum Access

This paper focuses on spectrum management in next generation of cellular networks. Several concepts are introduced that are central to the design of spectrum management algorithms. A practically realizable candidate algorithm for spectrum pricing is introduced based on pricing models and economic concepts. A peak-load pricing scheme with combinatorial auctions is suggested. Peak-load pricing raises prices when the demand for a service is at its highest. The winners of these auctions will be decided by a winner determination algorithm. Further investigation is conducted, testing the results.

CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions

Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is 𝒩𝒫-complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster—especially in cases with structure. CABOB's search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem—the run-time distribution does not have a heavy tail.

Bundle Design in Robust Combinatorial Auction Protocol against False-name Bids

This paper presents a method for designing bundles in a combinatorial auction protocol that is robust against false-name bids. Internet auctions have become an integral part of Electronic Commerce and a promising field for applying AI technologies. However, the possibility of a new type of cheating called a false-name bid, i.e., a bid submitted under a fictitious name, has been pointed out. A protocol called Leveled Division Set (LDS) protocol that is robust against false-name bids has been developed. However, this protocol requires the auctioneer to define a leveled division set. A leveled division set is a series of division sets, where a division set is a set of divisions and a division is a combination of bundles of goods. We need to solve a very complicated optimization problem to construct a leveled division set in order to obtain a good social surplus. We have developed a heuristic method for overcoming this problem. In this method, we first find a good division with a winner determination algorithm, and then construct a leveled division set by using this division as a seed. Through a simulation, we showthat our method can obtain a social surplus that is very close to optimal.

Algorithm for optimal winner determination in combinatorial auctions

Combinatorial auctions, that is, auctions where bidders can bid on combinations of items, tend to lead to more efficient allocations than traditional auction mechanisms in multi-item auctions where the agents' valuations of the items are not additive. However, determining the winners so as to maximize revenue is NP -complete. First, we analyze existing approaches for tackling this problem: exhaustive enumeration, dynamic programming, and restricting the allowable combinations. Second, we study the possibility of approximate winner determination, proving inapproximability in the general case, and discussing approximation algorithms for special cases. We then present our search algorithm for optimal winner determination. Experiments are shown on several bid distributions which we introduce. The algorithm allows combinatorial auctions to scale up to significantly larger numbers of items and bids than prior approaches to optimal winner determination by capitalizing on the fact that the space of bids is sparsely populated in practice. The algorithm does this by provably sufficient selective generation of children in the search tree, by using a secondary search for fast child generation, by using heuristics that are admissible and optimized for speed, and by preprocessing the search space in four ways. Incremental winner determination and quote computation techniques are presented. We show that basic combinatorial auctions only allow bidders to express complementarity of items. We then introduce two fully expressive bidding languages, called XOR-bids and OR-of-XORs, with which bidders can express general preferences (both complementarity and substitutability). The latter language is more concise. We show how these languages enable the use of the Vickrey–Clarke–Groves mechanism to construct a combinatorial auction where each bidder's dominant strategy is to bid truthfully. Finally, we extend our search algorithm and preprocessors to handle these languages as well as arbitrary XOR-constraints between bids.

An Efficient Approximate Algorithm for Winner Determination in Combinatorial Auctions

Auctions on the Internet have become especially popular in Electronic Commerce. Amongthe various studies on the Internet auctions, those on combinatorial auctions have lately attracted considerable attention. Combinatorial auctions simultaneously sell multiple items with interdependent values and allow the bidders to bid on any combination of items. Therefore, they tend to increase the buyers’ utilities and the seller’s revenue.