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In this paper, we consider the problem of designing incentive compatible auctions for multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints. When only the valuations are private and the budgets are public, Dobzinski <i>et al</i> [8] show that the <i>adaptive clinching</i> auction is the unique… (More)

While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of both time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a problem which lies at the core of many graph mining applications called densest subgraph problem. We develop an algorithm that… (More)

In commerce search, the set of products returned by a search engine often forms the basis for all user interactions leading up to a potential transaction on the web. Such a set of products is known as the <i>consideration set</i>. In this study, we consider the problem of generating consideration set of products in commerce search so as to maximize user… (More)

We present the first deterministic data structures for maintaining approximate minimum vertex cover and maximum matching in a fully dynamic graph G = (V,E), with |V | = n and |E| = m, in o( √ m ) time per update. In particular, for minimum vertex cover we provide deterministic data structures for maintaining a (2+ ) approximation inO(log n/ ) amortized time… (More)

In recent years, algorithms for computing game-theoretic solutions have been developed for real-world security domains. These games are between a defender, who must allocate her resources to defend potential targets, and an attacker, who chooses a target to attack. Existing work has assumed the set of defender’s resources to be fixed. This assumption… (More)

- Sayan Bhattacharya, Goutam Paul, Swagato Sanyal
- Discrete Applied Mathematics
- 2010

We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an ndimensional grid, at least n cops are necessary to ensure capture of the robber. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber. Further, for two-dimensional grid, we provide an… (More)

We consider the problem of a monopolist seller who wants to sell some items to a set of buyers. The buyers are strategic, unit-demand, and connected by a social network. Furthermore, the utility of a buyer is a decreasing function of the number of neighbors who do not own the item. In other words, they exhibit negative externalities, deriving utility from… (More)

We study the <i>price of anarchy</i> of coordination mechanisms for a scheduling problem where each job <i>j</i> has a weight <i>w<sub>j</sub></i>, processing time <i>p<sub>ij</sub></i>, assignment cost <i>h<sub>ij</sub></i>, and communication delay (or release date) <i>r<sub>ij</sub></i>, on machine <i>i</i>. Each machine is free to declare its own… (More)

We present two deterministic dynamic algorithms for the maximum matching problem. (1) An algorithm that maintains a (2+є)-approximate maximum matching in general graphs with <i>O</i>(<i>poly</i>(log<i>n</i>, 1/є)) update time. (2) An algorithm that maintains an α<sub><i>K</i></sub> approximation of the <em>value</em> of the maximum… (More)

While selfish routing has been studied extensively, the problem of designing better coordination mechanisms for routing over time in general graphs has remained an open problem. In this paper, we focus on tree networks (single source multiple destinations) with the goal of minimizing (weighted) average sojourn time of jobs, and provide the first… (More)