Julián Mestre

Why Do Hubs in the Yeast Protein Interaction Network Tend To Be Essential: Reexamining the Connection between the Network Topology and Essentiality

The centrality-lethality rule, which notes that high-degree nodes in a protein interaction network tend to correspond to proteins that are essential, suggests that the topological prominence of a protein in a protein interaction network may be a good predictor of its biological importance. Even though the correlation between degree and essentiality was confirmed by many independent studies, the reason for this correlation remains illusive. Several hypotheses about putative connections between essentiality of hubs and the topology of protein–protein interaction networks have been proposed, but as we demonstrate, these explanations are not supported by the properties of protein interaction networks. To identify the main topological determinant of essentiality and to provide a biological explanation for the connection between the network topology and essentiality, we performed a rigorous analysis of six variants of the genomewide protein interaction network for Saccharomyces cerevisiae obtained using different techniques. We demonstrated that the majority of hubs are essential due to their involvement in Essential Complex Biological Modules, a group of densely connected proteins with shared biological function that are enriched in essential proteins. Moreover, we rejected two previously proposed explanations for the centrality-lethality rule, one relating the essentiality of hubs to their role in the overall network connectivity and another relying on the recently published essential protein interactions model.

Greedy in approximation algorithms

The objective of this paper is to characterize classes of problems for which a greedy algorithm finds solutions provably close to optimum. To that end, we introduce the notion of k-extendible systems, a natural generalization of matroids, and show that a greedy algorithm is a 1 k-factor approximation for these systems. Many seemly unrelated problems fit in our framework, e.g.: b-matching, maximum profit scheduling and maximum asymmetric TSP. In the second half of the paper we focus on the maximum weight b-matching problem. The problem forms a 2-extendible system, so greedy gives us a -factor solution which runs in O(mlogn) time. We improve this by providing two linear time approximation algorithms for the problem: a -factor algorithm that runs in O(bm) time, and a (2 3- ()-factor algorithm which runs in expected O (nm log 1 ∈) time.

Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model

We study the maximum weight matching problem in the semi-streaming model, and improve on the currently best one-pass algorithm due to Zelke [Proceedings of the 25th Annual Symposium on Theoretical Aspects of Computer Science, 2008, pp. 669–680] by devising a deterministic approach whose performance guarantee is 4.91+e. In addition, we study preemptive online algorithms, a class of algorithms related to one-pass semi-streaming algorithms, where we are allowed to maintain only a feasible matching in memory at any point in time. We provide a lower bound of 4.967 on the competitive ratio of any such deterministic algorithm, and hence show that future improvements will have to store in memory a set of edges that is not necessarily a feasible matching. We conclude by presenting an empirical study, conducted in order to compare the practical performance of our approach to that of previously suggested algorithms.

To fill or not to fill: The gas station problem

In this article we study several routing problems that generalize shortest paths and the traveling salesman problem. We consider a more general model that incorporates the actual cost in terms of gas prices. We have a vehicle with a given tank capacity. We assume that at each vertex gas may be purchased at a certain price. The objective is to find the cheapest route to go from s to t, or the cheapest tour visiting a given set of locations. We show that the problem of finding a cheapest plan to go from s to t can be solved in polynomial time. For most other versions, however, the problem is NP-complete and we develop polynomial-time approximation algorithms for these versions.

Weighted popular matchings

We study the problem of assigning jobs to applicants. Each applicant has a weight and provides a <i>preference list</i>, which may contain ties, ranking a subset of the jobs. An applicant <i>x</i> may prefer one matching to another (or be indifferent between them, in case of a tie) based on the jobs <i>x</i> gets in the two matchings and <i>x</i>’s personal preference. A matching <i>M</i> is <i>popular</i> if there is no other matching <i>M</i>′ such that the weight of the applicants who prefer <i>M</i>′ to <i>M</i> exceeds the weight of those who prefer <i>M</i> to <i>M</i>′. We present algorithms to find a popular matching, or if none exists, to establish so. For instances with strict preference lists, we give an <i>O</i>(<i>n</i>+<i>m</i> time algorithm. For preference lists with ties, we give a more involved algorithm that solves the problem in <i>O</i>(min (<i>k</i> √<i>n</i>;, <i>n</i>) <i>m</i>) time, where <i>k</i> is the number of distinct weights the applicants are given.

Assigning Papers to Referees

Refereed conferences require every submission to be reviewed by members of a program committee (PC) in charge of selecting the conference program. There are many software packages available to manage the review process. Typically, in a bidding phase PC members express their personal preferences by ranking the submissions. This information is used by the system to compute an assignment of the papers to referees (PC members).We study the problem of assigning papers to referees. We propose to optimize a number of criteria that aim at achieving fairness among referees/papers. Some of these variants can be solved optimally in polynomial time, while others are NP-hard, in which case we design approximation algorithms. Experimental results strongly suggest that the assignments computed by our algorithms are considerably better than those computed by popular conference management software.

UNIVERSAL SEQUENCING ON AN UNRELIABLE MACHINE

We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. Our objective is to minimize wjf (Cj )f or any nondecreasing, nonnegative, differentiable cost function f (Cj ). We aim for a universal solution that performs well without adaptation for all cost functions for any possible machine behavior. We design a deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the machine behavior in advance. A randomized version of this algorithm attains in expectation a ratio of e .W e also show that both performance guarantees are best possible for any unbounded cost function. Our algorithms can be adapted to run in polynomial time with slightly increased cost. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n/ log log n) worse than an optimal sequence for any unbounded cost function. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a nontrivial algorithm with a small constant performance guarantee.

To fill or not to fill: the gas station problem

In this paper we study several routing problems that generalize shortest paths and the Traveling Salesman Problem. We consider a more general model that incorporates the actual cost in terms of gas prices. We have a vehicle with a given tank capacity. We assume that at each vertex gas may be purchased at a certain price. The objective is to find the cheapest route to go from s to t, or the cheapest tour visiting a given set of locations. Surprisingly, the problem of find the cheapest way to go from s to t can be solved in polynomial time and is not NP-complete. For most other versions however, the problem is NP-complete and we develop polynomial time approximation algorithms for these versions.

Universal sequencing on a single machine

We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. For the objective of minimizing the total weighted completion time, we design a polynomial time deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the disruptions in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. As a direct consequence of our results, we answer affirmatively the question of whether a constant approximation algorithm exists for the offline version of the problem when machine unavailability periods are known in advance. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(logn/ loglogn) worse than an optimal sequence. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a non-trivial algorithm with a small constant performance guarantee.

MobiTribe: Cost Efficient Distributed User Generated Content Sharing on Smartphones

Distributed social networking services show promise to solve data ownership and privacy problems associated with centralized approaches. Smartphones could be used for hosting and sharing users data in a distributed manner, if the associated high communication costs and battery usage issues of the distributed systems could be mitigated. We propose a novel mechanism for reducing these costs to a level comparable with centralized systems by using a connectivity aware replication strategy. We develop an algorithm for grouping devices into tribes for content replication among intended content consumers and serve it using low-cost network connections. We evaluate the performance of the algorithm using three real world trace data sets. The results show that a persistent low-cost network availability can be achieved with an average of two replicas per content. Additionally, cellular bandwidth consumption and energy consumption of users are evaluated analytically using user content creation and consumption modeling. The results show that the proposed mechanism lowers monetary and energy costs for users compared to non-mobile-optimized distributed systems irrespective of the content demand model.