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Kamesh Munagala

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37 papers
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37

AAAI Conference 2025 Conference Paper

Fair Division via the Cake-Cutting Share

  • Yannan Bai
  • Kamesh Munagala
  • Yiheng Shen
  • Ian Zhang

In this paper, we consider the classic fair division problem of allocating m divisible items to n agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the cake-cutting process. These shares generalize the notion of proportionality by taking into account the valuations of other agents via constraints capturing envy. We study what fraction (approximation) of these shares are achievable in the worst case, and present tight and non-trivial approximation bounds as a function of n and m. In particular, we show a tight approximation bound of Θ(√n) for various notions of such shares. We show this bound via a novel application of dual fitting, which may be of independent interest. We also present a bound of O(m^(2/3)) for a strict notion of share, with an almost matching lower bound. We further develop weaker notions of shares whose approximation bounds interpolate smoothly between proportionality and the shares described above. We finally present empirical results showing that our definitions lead to more reasonable shares than the standard fair share notion of proportionality.

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ICML Conference 2024 Conference Paper

Individual Fairness in Graph Decomposition

  • Kamesh Munagala
  • Govind S. Sankar

In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters that are cohesive in that close by pairs of nodes are assigned to the same cluster with high probability. We consider the additional aspect of individual fairness – pairs of nodes at comparable distances should be separated with comparable probability. We show that classic decomposition procedures do not satisfy this property. We present novel algorithms that achieve various trade-offs between this property and additional desiderata of connectivity of the clusters and optimality in number of clusters. We show that our individual fairness bounds may be difficult to improve by tying the improvement to resolving a major open question in metric embeddings. We finally show the efficacy of our algorithms on real planar networks modeling Congressional redistricting.

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AAMAS Conference 2023 Conference Paper

Fairness in the Assignment Problem with Uncertain Priorities

  • Zeyu Shen
  • Zhiyi Wang
  • Xingyu Zhu
  • Brandon Fain
  • Kamesh Munagala

In the assignment problem, a set of items must be allocated to unitdemand agents who express ordinal preferences (rankings) over the items. In the assignment problem with priorities, agents with higher priority are entitled to their preferred goods with respect to lower priority agents. A priority can be naturally represented as a ranking and an uncertain priority as a distribution over rankings. For example, this models the problem of assigning student applicants to university seats or job applicants to job openings when the admitting body is uncertain about the true priority over applicants. This uncertainty can express the possibility of bias in the generation of the priority ranking. We believe we are the first to explicitly formulate and study the assignment problem with uncertain priorities. We introduce two natural notions of fairness in this problem: stochastic envy-freeness (SEF) and likelihood envy-freeness (LEF). We show that SEF and LEF are incompatible and that LEF is incompatible with ordinal efficiency. We describe two algorithms, Cycle Elimination (CE) and Unit-Time Eating (UTE) that satisfy ordinal efficiency (a form of ex-ante Pareto optimality) and SEF; the well known random serial dictatorship algorithm satisfies LEF and the weaker efficiency guarantee of ex-post Pareto optimality. We also show that CE satisfies a relaxation of LEF that we term 1-LEF which applies only to certain comparisons of priority, while UTE satisfies a version of proportional allocations with ranks. We conclude by demonstrating how a mediator can model a problem of school admission in the face of bias as an assignment problem with uncertain priority.

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NeurIPS Conference 2022 Conference Paper

All Politics is Local: Redistricting via Local Fairness

  • Shao-Heng Ko
  • Erin Taylor
  • Pankaj Agarwal
  • Kamesh Munagala

In this paper, we propose to use the concept of local fairness for auditing and ranking redistricting plans. Given a redistricting plan, a deviating group is a population-balanced contiguous region in which a majority of individuals are of the same interest and in the minority of their respective districts; such a set of individuals have a justified complaint with how the redistricting plan was drawn. A redistricting plan with no deviating groups is called locally fair. We show that the problem of auditing a given plan for local fairness is NP-complete. We present an MCMC approach for auditing as well as ranking redistricting plans. We also present a dynamic programming based algorithm for the auditing problem that we use to demonstrate the efficacy of our MCMC approach. Using these tools, we test local fairness on real-world election data, showing that it is indeed possible to find plans that are almost or exactly locally fair. Further, we show that such plans can be generated while sacrificing very little in terms of compactness and existing fairness measures such as competitiveness of the districts or seat shares of the plans.

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SODA Conference 2022 Conference Paper

Approximate Core for Committee Selection via Multilinear Extension and Market Clearing

  • Kamesh Munagala
  • Yiheng Shen 0001
  • Kangning Wang 0001
  • Zhiyi Wang

Motivated by civic problems such as participatory budgeting and multiwinner elections, we consider the problem of public good allocation: Given a set of indivisible projects (or candidates) of different sizes, and voters with different monotone utility functions over subsets of these candidates, the goal is to choose a budget-constrained subset of these candidates (or a committee) that provides fair utility to the voters. The notion of fairness we adopt is that of core stability from cooperative game theory: No subset of voters should be able to choose another blocking committee of proportionally smaller size that provides strictly larger utility to all voters that deviate. The core provides a strong notion of fairness, subsuming other notions that have been widely studied in computational social choice. It is well-known that an exact core need not exist even when utility functions of the voters are additive across candidates. We therefore relax the problem to allow approximation: Voters can only deviate to the blocking committee if after they choose any extra candidate (called an additament ), their utility still increases by an α factor. If no blocking committee exists under this definition, we call this an α -core. Our main result is that an α -core, for α < 67. 37, always exists when utilities of the voters are arbitrary monotone submodular functions, and this can be computed in polynomial time. This result improves to α < 9. 27 for additive utilities, albeit without the polynomial time guarantee. Our results are a significant improvement over prior work that only shows logarithmic approximations for the case of additive utilities. We complement our results with a lower bound of α > 1. 015 for submodular utilities, and a lower bound of any function in the number of voters and candidates for general monotone utilities.

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AAAI Conference 2022 Conference Paper

Locally Fair Partitioning

  • Pankaj K. Agarwal
  • Shao-Heng Ko
  • Kamesh Munagala
  • Erin Taylor

We model the societal task of redistricting political districts as a partitioning problem: Given a set of n points in the plane, each belonging to one of two parties, and a parameter k, our goal is to compute a partition Π of the plane into regions so that each region contains roughly σ = n/k points. Π should satisfy a notion of “local” fairness, which is related to the notion of core, a well-studied concept in cooperative game theory. A region is associated with the majority party in that region, and a point is unhappy in Π if it belongs to the minority party. A group D of roughly σ contiguous points is called a deviating group with respect to Π if majority of points in D are unhappy in Π. The partition Π is locally fair if there is no deviating group with respect to Π. This paper focuses on a restricted case when points lie in 1D. The problem is non-trivial even in this case. We consider both adversarial and “beyond worst-case” settings for this problem. For the former, we characterize the input parameters for which a locally fair partition always exists; we also show that a locally fair partition may not exist for certain parameters. We then consider input models where there are “runs” of red and blue points. For such clustered inputs, we show that a locally fair partition may not exist for certain values of σ, but an approximate locally fair partition exists if we allow some regions to have smaller sizes. We finally present a polynomialtime algorithm for computing a locally fair partition if one exists.

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NeurIPS Conference 2021 Conference Paper

Robust Allocations with Diversity Constraints

  • Zeyu Shen
  • Lodewijk Gelauff
  • Ashish Goel
  • Aleksandra Korolova
  • Kamesh Munagala

We consider the problem of allocating divisible items among multiple agents, and consider the setting where any agent is allowed to introduce {\emph diversity constraints} on the items they are allocated. We motivate this via settings where the items themselves correspond to user ad slots or task workers with attributes such as race and gender on which the principal seeks to achieve demographic parity. We consider the following question: When an agent expresses diversity constraints into an allocation rule, is the allocation of other agents hurt significantly? If this happens, the cost of introducing such constraints is disproportionately borne by agents who do not benefit from diversity. We codify this via two desiderata capturing {\em robustness}. These are {\emph no negative externality} -- other agents are not hurt -- and {\emph monotonicity} -- the agent enforcing the constraint does not see a large increase in value. We show in a formal sense that the Nash Welfare rule that maximizes product of agent values is {\emph uniquely} positioned to be robust when diversity constraints are introduced, while almost all other natural allocation rules fail this criterion. We also show that the guarantees achieved by Nash Welfare are nearly optimal within a widely studied class of allocation rules. We finally perform an empirical simulation on real-world data that models ad allocations to show that this gap between Nash Welfare and other rules persists in the wild.

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NeurIPS Conference 2020 Conference Paper

Adaptive Probing Policies for Shortest Path Routing

  • Aditya Bhaskara
  • Sreenivas Gollapudi
  • Kostas Kollias
  • Kamesh Munagala

Inspired by traffic routing applications, we consider the problem of finding the shortest path from a source $s$ to a destination $t$ in a graph, when the lengths of the edges are unknown. Instead, we are given {\em hints} or predictions of the edge lengths from a collection of ML models, trained possibly on historical data and other contexts in the network. Additionally, we assume that the true length of any candidate path can be obtained by {\em probing} an up-to-date snapshot of the network. However, each probe introduces a latency, and thus the goal is to minimize the number of probes while finding a near-optimal path with high probability. We formalize this problem and show assumptions under which it admits to efficient approximation algorithms. We verify these assumptions and validate the performance of our algorithms on real data.

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STOC Conference 2020 Conference Paper

Approximately stable committee selection

  • Zhihao Jiang
  • Kamesh Munagala
  • Kangning Wang 0001

In the committee selection problem, we are given m candidates, and n voters. Candidates can have different weights. A committee is a subset of candidates, and its weight is the sum of weights of its candidates. Each voter expresses an ordinal ranking over all possible committees. The only assumption we make on preferences is monotonicity: If S ⊆ S ′ are two committees, then any voter weakly prefers S ′ to S . We study a general notion of group fairness via stability: A committee of given total weight K is stable if no coalition of voters can deviate and choose a committee of proportional weight, so that all these voters strictly prefer the new committee to the existing one. Extending this notion to approximation, for parameter c ≥ 1, a committee S of weight K is said to be c -approximately stable if for any other committee S ′ of weight K ′, the fraction of voters that strictly prefer S ′ to S is strictly less than c K ′/ K . When c = 1, this condition is equivalent to classical core stability. The question we ask is: Does a c -approximately stable committee of weight at most any given value K always exist for constant c ? It is relatively easy to show that there exist monotone preferences for which c ≥ 2. However, even for simple and widely studied preference structures, a non-trivial upper bound on c has been elusive. In this paper, we show that c = O (1) for all monotone preference structures. Our proof proceeds via showing an existence result for a randomized notion of stability, and iteratively rounding the resulting fractional solution.

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IJCAI Conference 2020 Conference Paper

Concentration of Distortion: The Value of Extra Voters in Randomized Social Choice

  • Brandon Fain
  • William Fan
  • Kamesh Munagala

We study higher statistical moments of Distortion for randomized social choice in a metric implicit utilitarian model. The Distortion of a social choice mechanism is the expected approximation factor with respect to the optimal utilitarian social cost (OPT). The k'th moment of Distortion is the expected approximation factor with respect to the k'th power of OPT. We consider mechanisms that elicit alternatives by randomly sampling voters for their favorite alternative. We design two families of mechanisms that provide constant (with respect to the number of voters and alternatives) k'th moment of Distortion using just k samples if all voters can then participate in a vote among the proposed alternatives, or 2k-1 samples if only the sampled voters can participate. We also show that these numbers of samples are tight. Such mechanisms deviate from a constant approximation to OPT with probability that drops exponentially in the number of samples, independent of the total number of voters and alternatives. We conclude with simulations on real-world Participatory Budgeting data to qualitatively complement our theoretical insights.

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JAIR Journal 2019 Journal Article

Iterative Local Voting for Collective Decision-making in Continuous Spaces

  • Nikhil Garg
  • Vijay Kamble
  • Ashish Goel
  • David Marn
  • Kamesh Munagala

Many societal decision problems lie in high-dimensional continuous spaces not amenable to the voting techniques common for their discrete or single-dimensional counterparts. These problems are typically discretized before running an election or decided upon through negotiation by representatives. We propose a algorithm called Iterative Local Voting for collective decision-making in this setting. In this algorithm, voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm, with the size of the ball shrinking at a specified rate. We first prove the convergence of this algorithm under appropriate choices of neighborhoods to Pareto optimal solutions with desirable fairness properties in certain natural settings: when the voters' utilities can be expressed in terms of some form of distance from their ideal solution, and when these utilities are additively decomposable across dimensions. In many of these cases, we obtain convergence to the societal welfare maximizing solution.We then describe an experiment in which we test our algorithm for the decision of the U.S. Federal Budget on Mechanical Turk with over 2,000 workers, employing neighborhoods defined by various L-Norm balls. We make several observations that inform future implementations of such a procedure.

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ICML Conference 2019 Conference Paper

Proportionally Fair Clustering

  • Xingyu Chen
  • Brandon Fain
  • Liang Lyu 0001
  • Kamesh Munagala

We extend the fair machine learning literature by considering the problem of proportional centroid clustering in a metric context. For clustering n points with k centers, we define fairness as proportionality to mean that any n/k points are entitled to form their own cluster if there is another center that is closer in distance for all n/k points. We seek clustering solutions to which there are no such justified complaints from any subsets of agents, without assuming any a priori notion of protected subsets. We present and analyze algorithms to efficiently compute, optimize, and audit proportional solutions. We conclude with an empirical examination of the tradeoff between proportional solutions and the k-means objective.

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AAAI Conference 2019 Conference Paper

Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice

  • Brandon Fain
  • Ashish Goel
  • Kamesh Munagala
  • Nina Prabhu

We study social choice mechanisms in an implicit utilitarian framework with a metric constraint, where the goal is to minimize Distortion, the worst case social cost of an ordinal mechanism relative to underlying cardinal utilities. We consider two additional desiderata: Constant sample complexity and Squared Distortion. Constant sample complexity means that the mechanism (potentially randomized) only uses a constant number of ordinal queries regardless of the number of voters and alternatives. Squared Distortion is a measure of variance of the Distortion of a randomized mechanism. Our primary contribution is the first social choice mechanism with constant sample complexity and constant Squared Distortion (which also implies constant Distortion). We call the mechanism Random Referee, because it uses a random agent to compare two alternatives that are the favorites of two other random agents. We prove that the use of a comparison query is necessary: no mechanism that only elicits the top-k preferred alternatives of voters (for constant k) can have Squared Distortion that is sublinear in the number of alternatives. We also prove that unlike any top-k only mechanism, the Distortion of Random Referee meaningfully improves on benign metric spaces, using the Euclidean plane as a canonical example. Finally, among top-1 only mechanisms, we introduce Random Oligarchy. The mechanism asks just 3 queries and is essentially optimal among the class of such mechanisms with respect to Distortion. In summary, we demonstrate the surprising power of constant sample complexity mechanisms generally, and just three random voters in particular, to provide some of the best known results in the implicit utilitarian framework.

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FOCS Conference 2015 Conference Paper

Competitive Flow Time Algorithms for Polyhedral Scheduling

  • Sungjin Im
  • Janardhan Kulkarni
  • Kamesh Munagala

Many scheduling problems can be viewed as allocating rates to jobs, subject to convex packing constraints on the rates. In this paper, we consider the problem of rate allocation when jobs of unknown size arrive online (non-clairvoyant setting), with the goal of minimizing weighted delay or flow time. Though this problem has strong lower bounds on competitive ratio in its full generality, we show positive results for natural and fairly broad sub-classes. More specifically, the subclasses we consider not only generalize several well-studied models such as scheduling with speedup curves and related machine scheduling, but also capture as special cases hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We establish several first positive results by making connections with two disparate disciplines: Economics and Queueing theory. First, we view the instantaneous allocation of rates as a resource allocation problem. We analyze the natural proportional fairness algorithm from economics. To do this, we extend results from market clearing literature, particularly the Eisenberg-Gale markets and the notions of Walrasian equilibria and Gross Substitutes. This yields the first constant competitive algorithm with constant speed augmentation for single-sink flow routing, routing multicast trees, and multidimensional resource allocation with substitutes resources. Next, we consider the general scheduling problem with packing constraints on rates, but with the restriction that the number of different job types is fixed. We model this problem as a non-stochastic queueing problem. We generalize a natural algorithm from queueing literature and analyze it by extending queueing theoretic ideas. We show that the competitive ratio, for any constant speed, depends polynomially only on the number of job types. Further, such a dependence on the number of job types is unavoidable for non-clairvoyant algorithms. This yields the first algorithm for scheduling multicommodity flows whose competitive ratio depends polynomially on the size of the underlying graph, and not on the number of jobs.

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FOCS Conference 2014 Conference Paper

SelfishMigrate: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors

  • Sungjin Im
  • Janardhan Kulkarni
  • Kamesh Munagala
  • Kirk Pruhs

We consider the classical problem of minimizing the total weighted flow-time for unrelated machines in the online non-clairvoyant setting. In this problem, a set of jobs J arrive over time to be scheduled on a set of M machines. Each job J has processing length pj, weight wj, and is processed at a rate of lij when scheduled on machine i. The online scheduler knows the values of wj and lij upon arrival of the job, but is not aware of the quantity pj. We present the first online algorithm that is scalable ((1+ε)-speed O(1/2)-competitive for any constant ε > 0) for the total weighted flow-time objective. No non-trivial results were known for this setting, except for the most basic case of identical machines. Our result resolves a major open problem in online scheduling theory. Moreover, we also show that no job needs more than a logarithmic number of migrations. We further extend our result and give a scalable algorithm for the objective of minimizing total weighted flow-time plus energy cost for the case of unrelated machines. In this problem, each machine can be sped up by a factor of f-1i(P) when consuming power P, where fi is an arbitrary strictly convex power function. In particular, we get an O(γ2)-competitive algorithm when all power functions are of form sγ. These are the first non-trivial non-clairvoyant results in any setting with heterogeneous machines. The key algorithmic idea is to let jobs migrate selfishly until they converge to an equilibrium. Towards this end, we define a game where each job's utility which is closely tied to the instantaneous increase in the objective the job is responsible for, and each machine declares a policy that assigns priorities to jobs based on when they migrate to it, and the execution speeds. This has a spirit similar to coordination mechanisms that attempt to achieve near optimum welfare in the presence of selfish agents (jobs). To the best our knowledge, this is the first work that demonstrates the usefulness of ideas from coordination mechanisms and Nash equilibria for designing and analyzing online algorithms.

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STOC Conference 2010 Conference Paper

Budget constrained auctions with heterogeneous items

  • Sayan Bhattacharya
  • Gagan Goel
  • Sreenivas Gollapudi
  • Kamesh Munagala

In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders have arbitrary demand and budget constraints (and additive valuations). Our mechanisms are surprisingly simple: We show that a sequential all-pay mechanism is a 4 approximation to the revenue of the optimal ex-interim truthful mechanism with a discrete type space for each bidder, where her valuations for different items can be correlated. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal ex-post truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sub-logarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles.

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FOCS Conference 2007 Conference Paper

Approximation Algorithms for Partial-Information Based Stochastic Control with Markovian Rewards

  • Sudipto Guha
  • Kamesh Munagala

We consider a variant of the classic multi-armed bandit problem (MAB), which we call feedback MAB, where the reward obtained by playing each of n independent arms varies according to an underlying on/off Markov process with known parameters. The evolution of the Markov chain happens irrespective of whether the arm is played, and furthermore, the exact state of the Markov chain is only revealed to the player when the arm is played and the reward observed. At most one arm (or in general, M arms) can be played any time step. The goal is to design a policy for playing the arms in order to maximize the infinite horizon time average expected reward. This problem is an instance of a partially observable Markov decision process (POMDP), and a special case of the notoriously intractable "restless bandit" problem. Unlike the stochastic MAB problem, the feedback MAB problem does not admit to greedy index-based optimal policies. Vie state of the system at any time step encodes the beliefs about the states of different arms, and the policy decisions change these beliefs - this aspect complicates the design and analysis of simple algorithms. We design a constant factor approximation to the feedback MAB problem by solving and rounding a natural LP relaxation to this problem. As far as we are aware, this is the first approximation algorithm for a POMDP problem.

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FOCS Conference 2001 Conference Paper

Designing Networks Incrementally

  • Adam Meyerson
  • Kamesh Munagala
  • Serge A. Plotkin

We consider the problem of incrementally designing a network to route demand to a single sink on an underlying metric space. We are given cables whose costs per unit length scale in a concave fashion with capacity. Under certain natural restrictions on the costs (called the Access Network Design constraints), we present a simple and efficient randomized algorithm that is competitive to the minimum cost solution when the demand points arrive online. In particular, if the order of arrival is a random permutation, we can prove a O(1) competitive ratio. For the fully adversarial case, the algorithm is O(K) -competitive, where K is the number of different pipe types. Since the value of K is typically small, this improves the previous O(log n log log n)-competitive algorithm which was based on probabilistically approximating the underlying metric by a tree metric. Our algorithm also improves the best known approximation ratio and running time for the offline version of this problem.

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FOCS Conference 2000 Conference Paper

Cost-Distance: Two Metric Network Design

  • Adam Meyerson
  • Kamesh Munagala
  • Serge A. Plotkin

Presents the cost-distance problem, which consists of finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of source-sink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for the cost-distance problem, where k is the number of sources. We reduce several common network design problems to cost-distance problems, obtaining (in some cases) the first known logarithmic approximation for them. These problems include a single-sink buy-at-bulk problem with variable pipe types between different sets of nodes, facility location with buy-at-bulk-type costs on edges, constructing single-source multicast trees with good cost and delay properties, and multi-level facility location. Our algorithm is also easier to implement and significantly faster than previously known algorithms for buy-at-bulk design problems.

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FOCS Conference 2000 Conference Paper

Hierarchical Placement and Network Design Problems

  • Sudipto Guha
  • Adam Meyerson
  • Kamesh Munagala

Gives constant approximations for a number of layered network design problems. We begin by modeling hierarchical caching, where the caches are placed in layers and each layer satisfies a fixed percentage of the demand (bounded miss rates). We present a constant approximation to the minimum total cost of placing the caches and to the routing demand through the layers. We extend this model to cover more general layered caching scenarios, giving a constant combinatorial approximation to the well-studied multi-level facility location problem. We consider a facility location variant, the load-balanced facility location problem, in which every demand is served by a unique facility and each open facility must serve at least a certain amount of demand. By combining load-balanced facility location with our results on hierarchical caching, we give a constant approximation for the access network design problem.

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