To browse Academia. Skip to main content. Log In Sign Up. Seeun Umboh. Secretary Problems with Convex Costs. Requests are presented online in random order, and each request possesses an adversarial value and an adversarial size. This problem falls within the framework of secretary problems. Unlike previous work in that area, one of the main challenges we face is that the objective function can be positive or negative and we must guard against accepting requests that look volvo v70 center console removal early on but cause the solution to have an arbitrarily large cost as more requests are accepted.

This requires designing new techniques. We study this problem under various feasibility constraints and present online algorithms with com- petitive ratios only a constant factor worse than those known in the absence of costs for the same feasi- bility constraints. We also consider a multi-dimensional version of the problem that generalizes multi- dimensional knapsack within a secretary framework.

This model captures, for example, the optimization problem faced by a cloud computing service accepting jobs, a wireless access point accepting connections from mobile nodes, or an advertiser in a sponsored search auction deciding which keywords to bid on. In many of these settings, the server must make accept or reject decisions in an online fashion as soon as requests are received without knowledge of the quality future requests.

A classical example of online decision making is the secretary problem. Here a company is interested in hiring a candidate for a single position; candidates arrive for interview in random order, and the company must accept or reject each candidate following the interview. The goal is to select the best candidate as often as possible. What makes the problem challenging is that each interview merely reveals the rank of the candidate relative to the ones seen previously, but not the ones following.

More general resource allocation settings may allow picking multiple candidates subject to a certain feasibility constraint. Here F denotes a feasibility constraint that the set of accepted requests must satisfy e. For such a sum-of-values objective, constant factor competitive ratios are known for various kinds of feasibility constraints including cardinality constraints [17, 19], knapsack constraints [4], and certain matroid constraints [5]. In many settings, the linear sum-of-values objective does not adequately capture the tradeoffs that the server faces in accepting or rejecting a request, and feasibility constraints provide only a rough approxima- tion.

Consider, for example, a wireless access point accepting connections. Each accepted request improves resource utilization and brings value to the access point. However as the number of accepted requests grows the access point performs greater multiplexing of the spectrum, and must use more and more transmitting power in order to maintain a reasonable connection bandwidth for each request. The power consumption and its associated cost are non-linear functions of the total load on the access point.

This directly translates into a value minus cost type of objective function where the cost is an increasing function of the load or total size of all the requests accepted. We consider the profit maximization problem under various feasibility constraints. For single-dimensional costs, we obtain online algorithms with competitive ratios within a constant factor of those achievable for a sum-of-values objective with the same feasibility constraints.

We remark that this is essentially the best approximation achievable even in the offline setting: Dean et al. Improving this factor is a possible avenue for future research. Recently several works [13, 6, 16] have looked at secretary problems with submodular objective functions and developed constant competitive algo- rithms. In the case of [6] and [16], the objective function is not necessarily monotone.

Nevertheless, nonnegativity implies that the universe of elements can be divided into two parts, over each of which the objective essentially behaves like a monotone submodular function in the sense that adding extra elements to a good subset of the optimal solution does not decrease its objective function value.

In our setting, in contrast, adding elements with too large a size to the solution can cause the cost of the solution to become too large and therefore imply a negative profit, even if the rest of the elements are good in terms of their value-size tradeoff. This necessitates designing new techniques.

Our techniques.I do not know how you feel about it, but you were a male in your last earthly incarnation. You were born somewhere around the territory of Ireland approximately on Your profession was banker, usurer, moneylender, and judge. Psychologically, you had a Bohemian personality - mysterious, highly gifted, capable of understanding ancient books.

Magical abilities, could be a servant of dark forces. Your problem - to learn to love and to trust the Universe. You are bound to think, study, reflect and develop inner wisdom. Toggle navigation. Name Poster. On This Page. How to Pronounce Seeun.

Is this an accurate pronunciation? How difficult is it to pronounce Seeun? Can Seeun be pronounced multiple ways? Record your pronunciation Recording. Click to stop. We noticed you have a microphone. If you know how to pronounce Seeun, just click the button to record. We'll save it, review it, and post it to help others. Recordings from children under 18 are not allowed. Back to Top. Meaning and Origin What does the name Seeun mean? Find out below.

Origin and Meaning of Seeun.

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User Submitted Origins. Seeun Means. Cited Source. We will review your submission shortly! Fun Facts about the name Seeun How unique is the name Seeun? Out of 6, records in the U.

Social Security Administration public data, the first name Seeun was not present. It is possible the name you are searching has less than five occurrences per year. Weird things about the name Seeun: Your name in reverse order is Nuees. A random rearrangement of the letters in your name anagram will give Seneu.A list of active members and alumni of the Theory of Computing group. Computational number theory and algebra, analysis of randomized and quantum algorithms, cryptography.

Algorithms for combinatorial, stochastic, and online optimization; applications to economics; algorithmic mechanism design; learning theory.

Complexity theory: lower bounds for NP-complete problems, pseudorandomness and derandomization, quantum computing. Algorithmic game theory and mechanism design, learning theory, fine-grained complexity. Algorithms for combinatorial, stochastic, and online optimization. Data processing, data pricing, and managing data under uncertainty. Computability theory and applications to model theory. Thesis: Approximations in Bayesian mechanism design for multi-parameter settings.

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Theory of Computing. People Courses Events. People Faculty. Eric Bach CS bach cs. Jin-Yi Cai CS jyc cs. Shuchi Chawla CS shuchi cs. Ilias Diakonikolas CS ilias cs. Dieter van Melkebeek CS dieter cs. Christos Tzamos CS tzamos cs. Alberto Del Pia Algorithms for combinatorial, stochastic, and online optimization.

Paris Koutris Data processing, data pricing, and managing data under uncertainty. Steffen Lempp Computability theory and applications to model theory. Sebastien Roch Applied probability, statistics. Ali Vakilian vakilian mit.

Jialu Bao jialu cs. Evangelia Gergatsouli gergatsouli wisc. Artem Govorov hovarau wisc. Vasilis Kontonis kontonis wisc.

### Faculty and Students

Tianyu Liu tl cs. Jeremy McMahan jmcmahan wisc. Andrew Morgan amorgan wisc. Jongho Park jongho. Rojin Rezvan rezvansangsa wisc. Nicollas Sdroievski sdroievski wisc. Shuai Shao sh cs.Nikhil Bansal, Anupam Gupta. Algorithmic Aspects of Discrepancy. Chapter in the book Panorama of Discrepancy Theory.

New developments in iterated rounding. Notes for IPCO summer school lec1lec2, slidesexercises. Randomized Algorithms Sp Some lecture notes. Dagstuhl Seminar on Scheduling, Feb Scheduling under UncertaintyJuneEindhoven.

Geometry of scheduling on multiple machines.

Nikhil Bansal, Jatin Batra. Online vector balancing and geometric discrepancy. On-line balancing of random inputs. Nikhil Bansal, Joel Spencer. SODA Potential-Function Proofs for Gradient Methods. Theory of Computing New notions and constructions of sparsification for graphs and hypergraphs.

FOCS On a generalization of iterated and randomized rounding. Nikhil Bansal. STOC On the discrepancy of random low degree set systems. Achievable performance of blind policies in heavy traffic. Math of OR 43 3, Competitive Algorithms for Generalized k-server in uniform metrics. Nested Convex Bodies are Chaseable.Any time.

## Nikhil Bansal

Title Keywords Abstract Author All. Show Search My Library. Any time 1 1 1 1 Custom range Display every page 5 10 20 Item. Online Network Design Algorithms via Hierarchical Decompositions Seeun Umboh Computer Science, Abstract : We develop a new approach for online network design and obtain improved competitive ratios for several problems. Our approach gives natural deterministic algorithms and simple analyses.

At the heart of our work is a novel application of embeddings into hierarchically well-separated trees HSTs to the analysis of online network design algorithms we charge the cost of the algorithm to the cost of the optimal solution on any HST embedding of the terminals. This analysis technique is widely applicable to many problems and gives a unified framework for online network design.

In a sense, our work brings together two of the main approaches to online network design. The first uses greedy-like algorithms and analyzes them using dual-fitting. Our approach uses deterministic greedy-like algorithms but analyzes them via HST embeddings of the terminals. We match the competitive ratio first achieved by Qian and Williamson and give a simpler analysis. Abstract : We consider the following sample selection problem. We observe in an online fashion a sequence of samples, each endowed by a quality.

Our goal is to either select or reject each sample, so as to maximize the aggregate quality of the subsample selected so far. There is a natural trade-off here between the rate of selection and the aggregate quality of the subsample. We show that for a number of such problems extremely simple and oblivious "threshold rules" for selection achieve optimal tradeoffs between rate of selection and aggregate quality in a probabilistic sense.

In some cases we show that the same threshold rule is optimal for a large class of quality distributions and is thus oblivious in a strong sense. Abstract : In the reordering buffer problem RBPa server is asked to process a sequence of requests lying in a metric space. To process a request the server must move to the corresponding point in the metric. The requests can be processed slightly out of order; in particular, the server has a buffer of capacity k which can store up to k requests as it reads in the sequence.

The goal is to reorder the requests in such a manner that the buffer constraint is satisfied and the total travel cost of the server is minimized.

The RBP arises in many applications that require scheduling with a limited buffer capacity, such as scheduling a disk arm in storage systems, switching colors in paint shops of a car manufacturing plant, and rendering 3D images in computer graphics.

## Seeun William Umboh

We study the offline version of RBP and develop bicriteria approximations. Constant factor approximations were known previously only for the uniform metric Avigdor-Elgrabli et al.

Via randomized tree embeddings, this implies an O log n approximation to cost and O 1 approximation to buffer size for general metrics. Previously the best known algorithm for arbitrary metrics by Englert et al.

Abstract : We study network design with a cost structure motivated by redundancy in data traffic.To protect your privacy, all features that rely on external API calls from your browser are turned off by default.

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Authors: no matches. Venues: no matches. Publications: no matches.We are given a graph, g groups of terminals, and a universe of data packets. Each group of terminals desires a subset of the packets from its respective source. The cost of routing traffic on any edge in the network is proportional to the total size of the distinct packets that the edge carries. Our goal is to find a minimum cost routing. We focus on two settings. In the first, the collection of packet sets desired by source-sink pairs is laminar.

In the second setting, packet sets can have non-trivial intersection. We focus on the case where each packet is desired by either a single terminal group or by all of the groups. Our approximation for the second setting is based on a novel spanner-type construction in unweighted graphs that, given a collection of g vertex subsets, finds a subgraph of cost only a constant factor more than the minimum spanning tree of the graph, such that every subset in the collection has a Steiner tree in the subgraph of cost at most O log g that of its minimum Steiner tree in the original graph.

We call such a subgraph a group spanner. Approximation, Randomization, and Combinatorial Optimization.

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