Rahul Sami

A BGP-based mechanism for lowest-cost routing

The routing of traffic between Internet domains or Autonomous Systems (ASs), a task known as interdomain routing, is currently handled by the Border Gateway Protocol (BGP). In this paper, we address the problem of interdomain routing from a mechanism-design point of view. The application of mechanism-design principles to the study of routing is the subject of earlier work by Nisan and Ronen [14] and Hershberger and Suri [10]. In this paper, we formulate and solve a version of the routing-mechanism design problem that is different from the previously studied version in three ways that make it more accurately reflective of real-world interdomain routing: (1) we treat the nodes as strategic agents, rather than the links; (2) our mechanism computes lowest-cost routes for all source-destination pairs and payments for transit nodes on all of the routes (rather than computing routes and payments for only one source-destination pair at a time, as is done in [14, 10]); (3) we show how to compute our mechanism with a distributed algorithm that is a straightforward extension to BGP and causes only modest increases in routing-table size and convergence time (in contrast with the centralized algorithms used in [14, 10]). This approach of using an existing protocol as a substrate for distributed computation may prove useful in future development of Internet algorithms generally, not only for routing or pricing problems. Our design and analysis of a strategyproof, BGP-based routing mechanism provides a new, promising direction in distributed algorithmic mechanism design, which has heretofore been focused mainly on multicast cost sharing.

Hardness results for multicast cost sharing

We continue the study of multicast cost sharing from the viewpoints of both computational complexity and economic mechanism design. We provide fundamental lower bounds on the network complexity of group-strategyproof, budget-balanced mechanisms. We also extend a classical impossibility result in game theory to show that no strategyproof mechanism can be both approximately efficient and approximately budget-balanced. Our results show that one important and natural case of multicast cost sharing is an example of a canonical hard problem in distributed, algorithmic mechanism design; in this sense, they represent progress toward the development of a complexity theory of Internet computation.

Approximation and collusion in multicast cost sharing

Abstract We investigate multicast cost sharing from both computational and economic perspectives. Recent work in economics leads to the consideration of two mechanisms: marginal cost (MC), which is efficient and strategyproof, and Shapley value (SH), which is budget-balanced and group-strategyproof. Subsequent work in computer science shows that the MC mechanism can be computed with only two modest-sized messages per link of the multicast tree but that computing the SH mechanism for p potential receivers can require Ω(p) bits of communication per link. We extend these results in two directions. First, we give a group-strategyproof mechanism that exhibits a tradeoff between the other properties of SH: It can be computed with exponentially lower worst-case communication than the SH algorithm, but it might fail to achieve exact budget balance (albeit by a bounded amount). Second, we completely characterize the groups that can strategize successfully against the MC mechanism.

Circuits for wide-window superscalar processors

Our program benchmarks and simulations of novel circuits indicate that large-window processors are feasible. Using our redesigned superscalar components, a large-window processor implemented in todays technology can achieve an increase of 10-60% (geometric mean of 31%) in program speed compared to todays processors. The processor operates at clock speeds comparable to todays processors, but achieves significantly higher ILP. To measure the impact of a large window on clock speed, we design and simulate new implementations of the logic components that most limit the critical path of our large-window processor: the schedule logic and the wake-up logic. We use log-depth cyclic segmented prefix (CSP) circuits to reimplement these components. Our layouts and simulations of critical paths through these circuits indicate that our large-window processor could be clocked at frequencies exceeding 500 MHz in todays technology. Our commit logic and rename logic can also run at these speeds. To measure the impact of a large window on ILP, we compare two microarchitectures, the first has a 128-instruction window, an 8-wide fetch unit, and 20-wide issue (four integer, branch, multiply, float, and memory units), whereas the second has a 32-instruction window, and a 4-wide fetch unit and is comparable to todays processors. For each, we simulate different window reuse and bypass policies. Our simulations show that the large-window processor achieves significantly higher IPC. This performance increase comes despite the fact that the large-window processor uses a wrap-around window while the small-window processor uses a compressing window, thus effectively increasing its number of outstanding instructions. Furthermore, the large-window processor sometimes pays an extra clock cycle for bypassing.

A sublinear algorithm for weakly approximating edit distance

We show how to determine whether the edit distance between two given strings is small in sublinear time. Specifically, we present a test which, given two n-character strings A and B, runs in time o(n) and with high probability returns CLOSE if their edit distance is O(nΑ), and FAR if their edit distance is Ω(n), where Α is a fixed parameter less than 1. Our algorithm for testing the edit distance works by recursively subdividing the strings A and B into smaller substrings and looking for pairs of substrings in A, B with small edit distance. To do this, we query both strings at random places using a special technique for economizing on the samples which does not pick the samples independently and provides better query and overall complexity. As a result, our test runs in time Õ(nmax(Α/2, 2Α - 1)) for any fixed Α < 1. Our algorithm thus provides a trade-off between accuracy and efficiency that is particularly useful when the input data is very large.We also show a lower bound of Ω(nΑ/2) on the query complexity of every algorithm that distinguishes pairs of strings with edit distance at most nΑ from those with edit distance at least n/6.

Distributed algorithmic mechanism design

Distributed algorithmic mechanism design (DAMD) is an approach to designing distributed systems that takes into account both the distributed-computational environment and the incentives of autonomous agents. In this dissertation, we study two problems, multicast cost sharing and interdomain routing. We also touch upon several issues important to DAMD in general, including approximation, compatibility with existing protocols, and hardness that results from the interplay of incentives and distributed computation. nThe multicast cost-sharing problem involves choosing a set of receivers for a multicast transmission and determining payments for them to offset the bandwidth costs of the multicast. We focus on cost-sharing mechanisms that are group-strategyproof and budget-balanced. We prove fundamental lower bounds on the network complexity of group-strategyproof mechanisms that are exactly or approximately budget-balanced. The Shapley-value mechanism (SH) is perhaps the most economically compelling mechanism in this class. We give a group-strategyproof mechanism that exhibits a tradeoff between the other properties of SH: It can be computed by an algorithm that is more communication-efficient than SH, but it might fail to achieve exact budget balance or exact minimum welfare loss (albeit by a bounded amount). We also show that no strategyproof mechanism for multicast cost sharing can be both approximately efficient and approximately budget-balanced. nInterdomain routing is the routing of traffic between Internet domains or Autonomous Systems, a task currently performed by the Border Gateway Protocol (BGP). We first show that there is a unique strategyproof mechanism for lowest-cost routing. Moreover, the prices required by this mechanism can be computed with a straightforward change to BGP that causes only modest increases in routing-table size and convergence time. nWe also formulate the policy routing mechanism-design problem. We show that, with arbitrary route valuations, it is NP-hard to find a welfare-maximizing (or even approximately welfare-maximizing) set of routes. For an important class of restricted valuations, next-hop preferences , a welfare-maximizing set of routes can be computed with a strategyproof mechanism in polynomial time (in a centralized computational model). However, we show that this mechanism appears to be incompatible with BGP, and hence is hard to compute in the context of the current Internet.

First-price path auctions

We study first-price auction mechanisms for auctioning flow between given nodes in a graph. A first-price auction is any auction in which links on winning paths are paid their bid amount; the designer has flexibility in specifying remaining details. We assume edges are independent agents with fixed capacities and costs, and their objective is to maximize their profit. We characterize all strong ε-Nash equilibria of a first-price auction, and show that the total payment is never significantly more than, and often less than, the well known dominant strategy Vickrey-Clark-Groves mechanism. We then present a randomized version of the first-price auction for which the equilibrium condition can be relaxed to ε-Nash equilibrium. We next consider a model in which the amount of demand is uncertain, but its probability distribution is known. For this model, we show that a simple ex ante first-price auction may not have any ε-Nash equilibria. We then present a modified mechanism with 2-parameter bids which does have an ε-Nash equilibrium. For a randomized version of this 2-parameter mechanism we characterize the set of all eNEs and prove a bound on the total payment in any eNE.

Computation in a distributed information market

According to economic theory--supported by empirical and laboratory evidence--the equilibrium price of a financial security reflects all of the information regarding the securitys value. We investigate the computational process on the path toward equilibrium, where information distributed among traders is revealed step-by-step over time and incorporated into the market price. We develop a simplified model of an information market, along with trading strategies, in order to formalize the computational properties of the process. We show that securities whose payoffs cannot be expressed as weighted threshold functions of distributed input bits are not guaranteed to converge to the proper equilibrium predicted by economic theory. On the other hand, securities whose payoffs are threshold functions are guaranteed to converge, for all prior probability distributions. Moreover, these threshold securities converge in at most n rounds, where n is the number of bits of distributed information. We also prove a lower bound, showing a type of threshold security that requires at least n/2 rounds to converge in the worst case.

Mechanism design for policy routing

The Border Gateway Protocol (BGP) for interdomain routing is designed to allow autonomous systems (ASes) to express policy preferences over alternative routes. We model these preferences as arising from an AS’s underlying utility for each route and study the problem of finding a set of routes that maximizes the overall welfare (ie, the sum of all ASes’ utilities for their selected routes).We show that, if the utility functions are unrestricted, this problem is NP-hard even to approximate closely. We then study a natural class of restricted utilities that we call next-hop preferences. We present a strategyproof, polynomial-time computable mechanism for welfare-maximizing routing over this restricted domain. However, we show that, in contrast to earlier work on lowest-cost routing mechanism design, this mechanism appears to be incompatible with BGP and hence difficult to implement in the context of the current Internet. Our contributions include a new complexity measure for Internet algorithms, dynamic stability, which may be useful in other problem domains.

Hardness Results for Multicast Cost Sharing

We continue the study of multicast cost sharing from the viewpoints of both computational complexity and economic mechanism design. We provide fundamental lower bounds on the network complexity of group-strategyproof, budget-balanced mechanisms. We also extend a classical impossibility result in game theory to show that no strategyproof mechanism can be both approximately efficient and approximately budget-balanced.