Anshul Kothari

Range addressable network: a P2P cache architecture for data ranges

Peer-to-peer computing paradigm is emerging as a scalable and robust model for sharing media objects. We propose an architecture and describe the associated algorithms and data structures to support the execution of range selection queries over data scattered across a P2P network especially for resource discovery in grid environments. We develop a distributed data structure referred to as a range addressable network that provides the following two quality-of-service guarantees: (i) the located peer is one with the smallest superset of the query range (important from the application perspective), and (ii) in a P2P network of n peers, a query is routed through O(log n) peers before the intended peer is found (important from the system perspective). Our preliminary experimental evaluation indicates that the range addressable network has desirable properties of scalability and load-balancing, which are crucial for the success of a large-scale P2P system.

Solving Combinatorial Exchanges: Optimality via a Few Partial Bids

Auctions have been studied in economics and game theory for a long time as important resource allocation mechanisms in distributed environments. In recent years, their role has grown with the emergence of Internet and electronic commerce, as businesses and corporations leverage the new medium to streamline their procurement process. Many businesses are moving to an auction-based purchase method where they issue a request for quotes for the goods and services needed, and let the suppliers bid for a piece of the business. Driven by these fundamentals, auctions and algorithms related to them have become important and popular research topics in computer science. An exchange generalizes the auction mechanism to the setting with multiple buyers and sellers. Some familiar examples are the exchanges for equities and commodities, transportation, electricity, and the businessto-business exchanges. A combinatorial exchange is an exchange where buyers and sellers can bid on bundles (subsets) of goods. Combinatorial markets are desirable because items often have complementarity, and combinatorial bidding minimizes bidders’ risk of getting stuck with only a partial subset. It also improves the overall economic efficiency.

Congestion games, load balancing, and price of anarchy

Imagine a set of self-interested clients, each of whom must choose a server from a permissible set. A servers latency is inversely proportional to its speed, but it grows linearly with (or, more generally, as the pth power of) the number of clients matched to it. Many emerging Internet-centric applications such as peer-to-peer networks, multi-player online games and distributed computing platforms exhibit such interaction of self-interested users. This interaction is naturally modeled as a congestion game, which we call server matching. In this overview paper, we summarize results of our ongoing work on the analysis of the server matching game, and suggest some promising directions for future research.

Bandwidth-Constrained Allocation in Grid Computing

Grid computing systems pool together the resources of many workstations to create a virtual computing reservoir. Users can “draw” resources using a pay-as-you-go model, commonly used for utilities (electricity and water). We model such a system as a capacitated graph, and study a basic allocation problem: given a set of jobs, each demanding computing and bandwidth resources and yielding a profit, determine which feasible subset of jobs yields the maximum total profit.

Server Allocation Algorithms for Tiered Systems

Many web-based systems have a tiered application architecture, in which a request needs to transverse all the tiers before finishing its processing. One of the most important QoS metrics for these applications is the expected response time for the user. Since the expected response time in any tier depends upon the number of servers allocated to this tier, and a requests total response time is the sum of the response times over all the tiers, many different configurations (number of servers allocated to each tier) can satisfy the expected response-time requirement. Naturally, one would like to find the configuration that minimizes the total system cost while satisfying the total response-time requirement. This is modeled as a non-linear optimization problem using an open-queuing network model of response time, which we call the server allocation problem for tiered systems (SAPTS). In this paper we study the computational complexity of SAPTS and design efficient algorithms to solve it. For a variable number of tiers, we show that the decision version of SAPTS is NP-complete. Then we design a simple two-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS). If the number of tiers is a constant, we show that SAPTS is polynomial-time solvable. Furthermore, we design a fast polynomial-time exact algorithm to solve the important two-tier case. Most of our results extend to the general case in which each tier has an arbitrary response-time function.

Interval subset sum and uniform-price auction clearing

We study the interval subset sum problem (ISSP), a generalization of the classic subset-sum problem, where given a set of intervals, the goal is to choose a set of integers, at most one from each interval, whose sum best approximates a target integer T. For the cardinality constrained interval subset-sum problem (kISSP), at least kmin and at most kmax integers must be selected. Our main result is a fully polynomial time approximation scheme for ISSP, with time and space both O(n . 1/e). For kISSP, we present a 2-approximation with time O(n), and a FPTAS with time O( n . kmax . 1/e ). Our work is motivated by auction clearing for uniform-price multi-unit auctions, which are increasingly used by security firms to allocate IPO shares, by governments to sell treasury bills, and by corporations to procure a large quantity of goods. These auctions use the uniform price rule – the bids are used to determine who wins, but all winning bidders receive the same price. For procurement auctions, a firm may even limit the number of winning suppliers to the range [kmin, kmax]. We reduce the auction clearing problem to ISSP, and use approximation schemes for ISSP to solve the original problem. The cardinality constrained auction clearing problem is reduced to kISSP and solved accordingly.

Server allocation algorithms for tiered systems

Many web-based systems have a tiered application architecture, in which a request needs to transverse all the tiers before finishing its processing. One of the most important QoS metrics for these applications is the expected response time for the user. Since the expected response time in any tier depends upon the number of servers allocated to this tier, and a request’s total response time is the sum of the response times at all the tiers, many different configurations (number of servers allocated to each tier) can satisfy the expected response time requirement. Naturally, one would like to find the configuration to minimize the total system cost while satisfying the total response time requirement. This is modeled as a non-linear optimization problem using an open-queuing network model of response time, which we call the server allocation problem for tiered systems (SAPTS). In this paper we study the computational complexity of SAPTS and design efficient algorithms to solve it. For a variable number of tiers, we show that the decision problem of SAPTS is NP-complete. Then we design a simple two-approximation algorithm and a fully polynomial time approximation scheme (FPTAS). If the number of tiers is a constant, we show that SAPTS is polynomial-time solvable. Furthermore, we design a fast polynomial-time exact algorithm to solve for the important two-tier case. Most of our results extend to the general case where each tier has an arbitrary response time function.