# Ramamoorthi RaviCarnegie Mellon University | CMU · Tepper School of Business

Ramamoorthi Ravi

## About

302

Publications

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8,510

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Introduction

Please look for my articles in my web page:
https://www.contrib.andrew.cmu.edu/~ravi/

**Skills and Expertise**

## Publications

Publications (302)

Problem definition: We consider the setting where a retailer with many physical stores and an online presence seeks to fulfill online orders using an omnichannel fulfillment program, such as buy-online ship-from-store. These fulfillment strategies try to minimize cost while fulfilling orders within acceptable service times. We focus on single-item...

We study the Weighted Tree Augmentation Problem for general link costs. We show that the integrality gap of the odd-LP relaxation for the (weighted) Tree Augmentation Problem for a k-level tree instance is at most 2−12k−1. For 2- and 3-level trees, these ratios are 32 and 74 respectively. Our proofs are constructive and yield polynomial-time approx...

Many applications such as hiring and university admissions involve evaluation and selection of applicants. These tasks are fundamentally difficult, and require combining evidence from multiple different aspects (what we term "attributes"). In these applications, the number of applicants is often large, and a common practice is to assign the task to...

Many applications such as hiring and university admissions involve evaluation and selection of applicants. These tasks are fundamentally difficult, and require combining evidence from multiple different aspects (what we term "attributes"). In these applications, the number of applicants is often large, and a common practice is to assign the task to...

We introduce and study a class of optimization problems we coin replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Nodes with capacity for storing a certain commodity are located at various places; at each node the commodity depletes within a certain time, the turnover time,...

We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates between sampling points from selected regions in the search space and de-emphasizing regions that may not lea...

In the Steiner Tree Augmentation Problem (STAP), we are given a graph $G = (V,E)$, a set of terminals $R \subseteq V$, and a Steiner tree $T$ spanning $R$. The edges $L := E \setminus E(T)$ are called links and have non-negative costs. The goal is to augment $T$ by adding a minimum cost set of links, so that there are 2 edge-disjoint paths between...

We consider the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We introduce and study a general downgrading variant of the interdiction problem where the capacity of an arc is a function of the subset of its endpoints that are d...

In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost cij of traveling from city i to city j, which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more tha...

We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates between sampling points from selected regions in the search space and de-emphasizing regions that may not lea...

The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed budget to increase the weight of edges in order to increase the weight of the MST as much as possible. Two popular...

We study a fundamental class of two-layer network design problems. A hub layer is configured by establishing hubs at selected nodes at considerable cost so that the routes between hubs can be operated cheaply. The remaining edges in the network are operated at regular cost. The resulting problem is to determine the set of nodes to open hubs and the...

We consider the 2-stage stochastic matroid base problem, where an initial set of elements is bought by paying their first-stage deterministic cost and then extended to a matroid base in the second stage after the scenario realization. The second-stage costs are unrelated to the first-stage costs and represented explicitly via a polynomial number of...

A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generali...

Dynamic pricing under unknown demand has been extensively studied but rarely deployed by real-world sellers, largely due to overlooking some practical constraints. For example, in most dynamic pricing policies, the prices may oscillate, which can potentially be highly undesirable. In many applications, retailers would not pursue extra revenues by i...

Problem definition: Omnichannel retailing has led to the use of traditional stores as fulfillment centers for online orders. Omnichannel fulfillment problems have two components: (1) accepting a certain number of online orders prior to seeing store demands and (2) satisfying (or filling) some of these accepted online demands as efficiently as possi...

We consider an information dissemination problem where the root of an undirected graph constantly updates its information and we wish to keep everyone in the graph as freshly informed about the root as possible. Our synchronous information spreading model uses telephone calls at each time step, in which any node can call at most one neighbor, thus...

We study the Weighted Tree Augmentation Problem for general link costs. We show that the integrality gap of the ODD-LP relaxation for the (weighted) Tree Augmentation Problem for a $k$-level tree instance is at most $2 - \frac{1}{2^{k-1}}$. For 2- and 3-level trees, these ratios are $\frac32$ and $\frac74$ respectively. Our proofs are constructive...

We consider the Unimodal Multi-Armed Bandit problem where the goal is to find the optimal price under an unknown unimodal reward function, with an additional "markdown" constraint that requires that the price exploration is non-increasing. This markdown optimization problem faithfully models a single-product revenue management problem where the obj...

The Moore-Hodgson Algorithm minimizes the number of late jobs on a single machine. That is, it finds an optimal schedule for the classical problem 1||∑Uj. Several proofs of the correctness of this algorithm have been published. We present a new short proof.

We consider the deterministic inventory routing problem over a discrete finite time horizon. Given clients on a metric, each with daily demands that must be delivered from a depot and holding costs over the planning horizon, an optimal solution selects a set of daily tours through a subset of clients to deliver all demands before they are due and m...

Problem Definition: Omni-channel retailing has led to the use of traditional stores as fulfillment centers for online orders. Omni-channel fulfillment problems have two components: (1) accepting a certain number of on-line orders prior to seeing store demands, and (2) satisfying (or filling) some of these accepted on-line demands as efficiently as...

We link the rapid and dramatic move from second-price to first-price auction format in the display advertising market to the move from the waterfalling mechanism employed by publishers for soliciting bids in a pre-ordered cascade over exchanges, to an alternate header bidding strategy that broadcasts the request for bid to all exchanges simultaneou...

We study the performance of a proportional weights algorithm for online capacitated bipartite matching modeling the delivery of impression ads. The algorithm uses predictions on the advertiser nodes to match arriving impression nodes fractionally in proportion to the weights of its neighbors. This paper gives a thorough empirical study of the perfo...

We combine ideas from uni-directional and bi-directional heuristic search, and approximation algorithms for the Traveling Salesman Problem, to develop a novel framework for a Multi-Goal Path Finding (MGPF) problem that provides a 2-approximation guarantee. MGPF aims to find a least-cost path from an origin to a destination such that each node in a...

The Moore-Hodgson Algorithm minimizes the number of late jobs on a single machine. That is, it finds an optimal schedule for the classical problem $1~|\;|~\sum{U_j}$. Several proofs of the correctness of this algorithm have been published. We present a new short proof.

We combine ideas from uni-directional and bi-directional heuristic search, and approximation algorithms for the Traveling Salesman Problem, to develop a novel framework for a Multi-Goal Path Finding (MGPF) problem that provides a 2-approximation guarantee. MGPF aims to find a least-cost path from an origin to a destination such that each node in a...

Given a graph, we wish to find a maximum number of vertex-disjoint paths of length 2. We propose a series of local improvement algorithms for this problem, and present a linear-programming based method for analyzing their performance.

We study a Multiple Depot Heterogeneous Traveling Salesman Problem (MDHTSP) where the cost of the traveling between any two targets depends on the type of the vehicle. The travel costs are assumed to be symmetric, satisfy the triangle inequality, and are monotonic, i.e., the travel costs between any two targets monotonically increases with the inde...

This paper proposes a new model for augmenting algorithms with useful predictions that go beyond worst-case bounds on the algorithm performance. By refining existing models, our model ensures predictions are formally learnable and instance robust. Learnability guarantees that predictions can be efficiently constructed from past data. Instance robus...

In the weighted minimum strongly connected spanning subgraph (WMSCSS) problem we must purchase a minimum-cost strongly connected spanning subgraph of a digraph. We show that half-integral linear program (LP) solutions for WMSCSS can be efficiently rounded to integral solutions at a multiplicative $1.5$ cost. This rounding matches a known $1.5$ inte...

In the weighted minimum strongly connected spanning subgraph (WMSCSS ) problem we must purchase a minimum-cost strongly connected spanning subgraph of a digraph. We show that half-integral linear program (LP) solutions for WMSCSS can be efficiently rounded to integral solutions at a multiplicative 1.5 cost. This rounding matches a known 1.5 integra...

We introduce and study the maximum reliability coverage problem, where multiple facilities are to be located on a network whose arcs are subject to random failures. Our model assumes that arcs fail independently with non-uniform probabilities, and the objective is to locate a given number of facilities, aiming to maximize the expected demand servic...

Although online advertising is the lifeline of many internet content platforms, the usage of ad blockers has surged in recent years, presenting a challenge to platforms dependent on ad revenue. Using a simple analytical model with two competing platforms, we show that the presence of ad blockers can actually benefit platforms. In particular, there...

We study the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We show hardness of obtaining strictly unicriterion approximations for this basic vertex interdiction problem. We also introduce and study a general downgrading variant...

Motivated by the well known “four-thirds conjecture” for the traveling salesman problem (TSP), we study the problem of uniform covers. A graph G=(V,E) has an α-uniform cover for TSP (2EC, respectively) if the everywhere α vector (i.e., {α}E) dominates a convex combination of incidence vectors of tours (2-edge-connected spanning multigraphs, respect...

We study problems that integrate depot location decisions along with the inventory routing problem of serving clients from these depots over time balancing the costs of routing vehicles from the depots with the holding costs of demand delivered before they are due. Since the inventory routing problem is already complex, we study the version that as...

A number of applications (e.g., AI bot tournaments, sports, peer grading, crowdsourcing) use pairwise comparison data and the Bradley-Terry-Luce (BTL) model to evaluate a given collection of items (e.g., bots, teams, students, search results). Past work has shown that under the BTL model, the widely-used maximum-likelihood estimator (MLE) is minima...

We study problems that integrate depot location decisions along with the inventory routing problem of serving clients from these depots over time balancing the costs of routing vehicles from the depots with the holding costs of demand delivered before they are due. Since the inventory routing problem is already complex, we study the version that as...

We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the 2-dimensional plane. Among other results, we give an O(n)approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We giv...

Recommender systems often operate on item catalogs clustered by genres, and user bases that have natural clusterings into user types by demographic or psychographic attributes. Prior work on system-wide diversity has mainly focused on defining intent-aware metrics among such categories and maximizing relevance of the resulting recommendations, but...

In this paper we study how to optimally balance cheap inflexible resources with more expensive, reconfigurable resources despite uncertainty in the input problem. Specifically, we introduce the MinEMax model to study "build versus rent" problems. In our model different scenarios appear independently. Before knowing which scenarios appear, we may bu...

We study the problem of locating facilities on the nodes of a network to maximize the expected demand serviced. The edges of the input graph are subject to random failure due to a disruptive event. We consider a special type of failure correlation. The edge dependency model assumes that the failure of a more reliable edge implies the failure of all...

Collaborative filtering is a broad and powerful framework for building recommendation systems that has seen widespread adoption. Over the past decade, the propensity of such systems for favoring popular products and thus creating echo chambers have been observed. This has given rise to an active area of research that seeks to diversify recommendati...

In this paper, we investigate the weighted tree augmentation problem (TAP), where the goal is to augment a tree with a minimum cost set of edges such that the graph becomes two edge connected. First we show that in weighted TAP, we can restrict our attention to trees which are binary and where all the non-tree edges go between two leaves of the tre...

We explore and introduce tools to design algorithms with improved approximation guarantees for edge connectivity problems such as the traveling salesman problem (TSP) and the 2-edge-connected spanning multigraph problem (2EC) on (restricted classes of) weighted graphs. In particular, we investigate decompositions of graphs that cover small-cardinal...

We study a generalization of the Steiner tree problem, where we are given a weighted network $G$ together with a collection of $k$ subsets of its vertices and a root $r$. We wish to construct a minimum cost network such that the network supports one unit of flow to the root from every node in a subset simultaneously. The network constructed does no...

In the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph $G=(V,E)$, edge costs $\{c_e\geq 0\}_{e\in E}$, terminal pairs $\{(s_i,t_i)\}_{i=1}^k$, and penalties $\{\pi_i\}_{i=1}^k$ for each terminal pair; the goal is to find a forest $F$ to minimize $c(F)+\sum_{i: (s_i,t_i)\text{ not connected in }F}\pi_i$. The Steiner...

We consider the problem of constructing optimal decision trees: given a collection of tests that can disambiguate between a set of m possible diseases, each test having a cost, and the a priori likelihood of any particular disease, what is a good adaptive strategy to perform these tests to minimize the expected cost to identify the disease? This pr...

Collaborative filtering is a broad and powerful framework for building recommendation systems that has seen widespread adoption. Over the past decade, the propensity of such systems for favoring popular products and thus creating echo chambers have been observed. This has given rise to an active area of research that seeks to diversify recommendati...

We introduce a new set of problems based on the Chain Editing problem. In our version of Chain Editing, we are given a set of anonymous participants and a set of undisclosed tasks that every participant attempts. For each participant-task pair, we know whether the participant has succeeded at the task or not. We assume that participants vary in the...

The online (uniform) buy-at-bulk network design problem asks us to design a network, where the edge-costs exhibit economy-of-scale. Previous approaches to this problem used tree-embeddings, giving us randomized algorithms. Moreover, the optimal results with a logarithmic competitive ratio requires the metric on which the network is being built to b...

We introduce a new set of problems based on the Chain Editing problem. In our version of Chain Editing, we are given a set of anonymous participants and a set of undisclosed tasks that every participant attempts. For each participant-task pair, we know whether the participant succeeded at the task or not. We assume that participants vary in their a...

We study the design of schedules for multi-commodity multicast. In this problem, we are given an undirected graph $G$ and a collection of source-destination pairs, and the goal is to schedule a minimum-length sequence of matchings that connects every source with its respective destination. Multi-commodity multicast models a classic information diss...

The online (uniform) buy-at-bulk network design problem asks us to design a network, where the edge-costs exhibit economy-of-scale. Previous approaches to this problem used tree- embeddings, giving us randomized algorithms. Moreover, the optimal results with a logarithmic competitive ratio requires the metric on which the network is being built to...

The revolution in big data has enabled a game-changing approach to marketing. The asynchronous and continuous collection of customer data carries rich signals about consumer preferences and consumption patterns. Use of this data can make marketing adaptive, dynamic, and responsive to changes in individual customer behavior. This book introduces sta...

We examine the effect of the presence of expert buyers on other buyers, the platform, and the sellers in online markets. We model buyer expertise as the ability to accurately predict the quality, or condition, of an item, modeled as its common value. We show that nonexperts may bid more aggressively, even above their expected valuation, to compensa...

We prove new results for approximating the Graphic TSP. Specifically, we provide a polynomial-time 9/7-approximation algorithm for cubic bipartite graphs and a (9/7 + 1/21(k-2))-approximation algorithm for k-regular bipartite graphs, both of which are improved approximation factors compared to previous results. Our approach involves finding a cycle...

We introduce group-to-group anycast (g2g-anycast), a network design problem of substantial practical importance and considerable generality. Given a collection of groups and requirements for directed connectivity from source groups to destination groups, the solution network must contain, for each requirement, an omni-directional down-link broadcas...

In the stochastic orienteering problem, we are given a finite metric space, where each node contains a job with some deterministic reward and a random processing time. The processing time distributions are known and independent across nodes. However the actual processing time of a job is not known until it is completely processed. The objective is...

Recommendations are central to the utility of many websites including
YouTube, Quora as well as popular e-commerce stores. Such sites typically
contain a set of recommendations on every product page that enables visitors to
easily navigate the website. Choosing an appropriate set of recommendations at
each page is one of the key features of backend...

The inventory routing problem involves trading off inventory holding costs at client locations with vehicle routing costs to deliver frequently from a single central depot to meet deterministic client demands over a finite planing horizon. In this paper, we consider periodic solutions that visit clients in one of several specified frequencies, and...

We present an approach for the traveling salesman problem with graph metric based on Steiner cycles. A Steiner cycle is a cycle that is required to contain some specified subset of vertices. For a graph \(G\), if we can find a spanning tree \(T\) and a simple cycle that contains the vertices with odd-degree in \(T\), then we show how to combine the...

We consider natural generalizations of the minimum broadcast time problem under the telephone model, where a rumor from a root node must be sent via phone calls to the whole graph in the minimum number of rounds; the telephone model implies that the set of edges involved in communicating in a round form a matching. The extensions we consider involv...

A tour in a graph is a connected walk that visits every vertex at least once, and returns to the starting vertex. Vishnoi (2012) proved that every connected d-regular graph with n vertices has a tour of length at most (1+o(1))n, where the o(1) term (slowly) tends to 0 as d grows. His proof is based on van-der-Warden’s conjecture (proved independent...

We consider the problem of designing efficient mechanisms to share the cost of providing some service to a set of self-interested customers. In this paper, we mainly focus on cost functions that are induced by prize-collecting optimization problems. Such cost functions arise naturally whenever customers can be served in two different ways: either b...

In this paper, we study the robust and stochastic versions of the two-stage min-cut and shortest path problems introduced in Dhamdhere et al. (in How to pay, come what may: approximation algorithms for demand-robust covering problems. In: FOCS, pp 367–378, 2005), and give approximation algorithms with improved approximation factors. Specifically, w...

We examine the effect of the presence of knowledgeable buyers (experts) in online markets where auctions with a hard close and posted prices are widely used. We model buyer expertise as the ability to accurately predict the quality, or condition, of an item. In auctions with a hard close, sniping – submitting bids in the last minute – emerges as an...

We prove new results for approximating Graphic TSP. Specifically, we provide
a polynomial-time \frac{9}{7}-approximation algorithm for cubic bipartite
graphs and a (\frac{9}{7}+\frac{1}{21(k-2)})-approximation algorithm for
k-regular bipartite graphs, both of which are improved approximation factors
compared to previous results. Our approach involv...

Detecting and quantifying the timing and the genetic contributions of parental populations to a hybrid population is an important but challenging problem in reconstructing evolutionary histories from genetic variation data. With the advent of high throughput genotyping technologies, new methods suitable for large-scale data are especially needed. F...

A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Many classical optimization problems, such as maximum spanning tree and forest, shortest path, maximum weight (perfect) matching, maximum weight independent set (basis) in a matroid or in the intersection of two matro...

Given an undirected graph with nonnegative edge weights, the max–min weighted TT-join problem is to find an even cardinality vertex subset TT such that the minimum weight TT-join for this set is maximum. The problem is NP-hard even on a cycle but permits a simple exact solution on trees. We present a 2/32/3-approximation algorithm based on a natura...

We consider minimizing a class of low rank quasi-concave functions over a convex set and give a fully polynomial time approximation scheme (FPTAS) for the problem. The algorithm is based on a binary search for the optimal objective value which is guided by solving a polynomial number of linear minimization problems over the convex set with appropri...

Transmission network expansion planning in its original formulation is NP-hard due to the subproblem Steiner trees, the minimum cost connection of an initially unconnected network with mandatory and optional nodes. By using electrical network theory we show why NP-hardness still holds when this subproblem of network design from scratch is omitted b...

Background:
Phylogeny estimation from aligned haplotype sequences has attracted more and more attention in the recent years due to its importance in analysis of many fine-scale genetic data. Its application fields range from medical research, to drug discovery, to epidemiology, to population dynamics. The literature on molecular phylogenetics prop...

Natural gas is distributed in the form of liquefied natural gas (LNG) when transported across long distances. Delivery planning of LNG offers challenging multi-origin vehicle routing problems, with vessels of various capacities and fuel performance. There are also unique challenges due to the nature of LNG trading and shipping. We propose a framewo...

Consider the following online version of the submodular maximization problem under a matroid constraint. We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent in the matroid over time. At each time, a new weighted rank function of a different matroid (one per time) over...

We consider packing LP’s with m rows where all constraint coefficients are normalized to be in the unit interval. The n columns arrive in random order and the goal is to set the corresponding decision variables irrevocably when they arrive to obtain a feasible solution maximizing the expected reward. Previous (1 − ε)-competitive algorithms require...

In the Stochastic Orienteering problem, we are given a metric, where each node also has a job located there with some deterministic reward and a random size. (Think of the jobs as being chores one needs to run, and the sizes as the amount of time it takes to do the chore.) The goal is to adaptively decide which nodes to visit to maximize total expe...

We consider the problem of finding a minimum edge cost subgraph of an
undirected or a directed graph satisfying given connectivity requirements and
degree bounds b(\cdot) on nodes. We present an iterative rounding algorithm of
the set-pair LP relaxation for this problem. When the graph is undirected and
the connectivity requirements are on the elem...

We study the distance constrained vehicle routing problem (DVRP) (Laporte et al., Networks 14 (1984), 47–61, Li et al., Oper Res 40 (1992), 790–799): given a set of vertices in a metric space, a specified depot, and a distance bound D, find a minimum cardinality set of tours originating at the depot that covers all vertices, such that each tour has...

In a setup where a divisible good is to be allocated to a set of bidders with budget constraints, we introduce a mechanism in the spirit of the Vickrey auction. In the mechanism we propose, understating budgets or values is weakly dominated. Since the revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuati...

We consider the vehicle routing problem with stochastic demands (VRPSD). We give randomized approximation algorithms achieving approximation guarantees of 1 + α for split-delivery VRPSD, and 2 + α for unsplit-delivery VRPSD; here a is the best approximation guarantee for the traveling salesman problem. These bounds match the best known for even the...