Qizhi Fang

Finding nucleolus of flow game

AbstractWe study the algorithmic issues of finding the nucleolus of a flow game. The flow game is a cooperative game defined on a network D=(V,E;ω). The player set is E and the value of a coalition S⊆E is defined as the value of a maximum flow from source to sink in the subnetwork induced by S. We show that the nucleolus of the flow game defined on a simple network (ω(e)=1 for each e∈E) can be computed in polynomial time by a linear program duality approach, settling a twenty-three years old conjecture by Kalai and Zemel. In contrast, we prove that both the computation and the recognition of the nucleolus are

On computational complexity of membership test in flow games and linear production games

\mathcal{NP}

Approximate and dynamic rank aggregation

-hard for flow games with general capacity.

Core stability of vertex cover games

Abstract. Let Γ≡(N,v) be a cooperative game with the player set N and characteristic function v: 2N→R. An imputation of the game is in the core if no subset of players could gain advantage by splitting from the grand coalition of all players. It is well known that, for the flow game (and equivalently, for the linear production game), the core is always non-empty and a solution in the core can be found in polynomial time. In this paper, we show that, given an imputation x, it is NP-complete to decide x is not a member of the core, for the flow game. And because of the specific reduction we constructed, the result also holds for the linear production game.

Membership for Core of LP Games and Other Games

Rank aggregation, originally an important issue in social choice theory, has become more and more important in information retrieval applications over the Internet, such as meta-search, recommendation system, etc. In this work, we consider an aggregation function using a weighted version of the normalized Kendall-τ distance. We propose a polynomial time approximation scheme, as well as a practical heuristic algorithm with the approximation ratio two for the NP-hard problem. In addition, we discuss issues and models for the dynamic rank aggregation problem.

Metasearch via Voting

In this paper, we focus on the core stability of vertex cover games, which arise from vertex cover problems on graphs. Based on duality theory of linear programming, we first prove that a balanced vertex cover game has the stable core if and only if every edge belongs to a maximum matching in the corresponding graph. We also show that for a totally balanced vertex cover game, the core largeness, extendability and exactness are all equivalent, which imply the core stability.

Condorcet Winners for Public Goods

Let Γ = (N, v) be a cooperative game with the player set N and characteristic function v : 2N → R. An imputation of the game is in the core if no subset of players could gain advantage by splitting from the grand coalition of all players. It is well known that, for the linear production game, and the flow game, the core is always non-empty (and a solution in the core can be found in polynomial time). In this paper, we show that, given an imputation x, it is NP-complete to decide it is not a member of the core, in both games. The same also holds for Steiner tree game. In addition, for Steiner tree games, we prove that testing the total balacedness is NP-hard.

A coordination mechanism for a scheduling game with parallel-batching machines

Metasearch engines are developed to overcome the shortcoming of single search engine and try to benefit from cooperative decision by combining the results of multiple independent search engines that make use of different models and configurations. In this work, we study the metasearch problem via voting that facilities multiple agents making cooperative decision. We can deem the source search engines as voters and all ranked documents as candidates, then metaseach problem is actually to find a voting algorithm to obtain group’s preferences on these documents(candidates). In addition to two widely discussed classical voting rules: Borda and Condorcet, we study another two voting algorithms, Black and Kemeny. Since Kemeny ranking problem is NP-hard, a new heuristic algorithm has been proposed for metasearch. Some experiments have been carried out on TREC2001 data for evaluating these metasearch algorithms coming from voting.

Majority equilibrium for public facility allocation

In this work, we consider a public facility allocation problem decided through a voting process under the majority rule. A location of the public facility is a majority rule winner if there is no other location in the network where more than half of the voters would have been closer to than the majority rule winner. We develop fast algorithms for interesting cases with nice combinatorial structures. We show that the computing problem and the decision problem in the general case, where the number of public facilities is more than one and is considered part of the input size, are all NP-hard. Finally, we discuss majority rule decision making for related models.

Total balancedness condition for Steiner tree games

In this paper we consider the scheduling problem with parallel-batching machines from a game theoretic perspective. There are m parallel-batching machines each of which can handle up to b jobs simultaneously as a batch. The processing time of a batch is the time required for processing the longest job in the batch, and all the jobs in a batch start and complete at the same time. There are n jobs. Each job is owned by a rational and selfish agent and its individual cost is the completion time of its job. The social cost is the largest completion time over all jobs, the makespan. We design a coordination mechanism for the scheduling game problem. We discuss the existence of pure Nash Equilibria and offer upper and lower bounds on the price of anarchy of the coordination mechanism. We show that the mechanism has a price of anarchy no more than