Adrian Vladu

Improved Parallel Algorithms for Spanners and Hopsets

We use exponential start time clustering to design faster parallel graph algorithms involving distances. Previous algorithms usually rely on graph decomposition routines with strict restrictions on the diameters of the decomposed pieces. We weaken these bounds in favor of stronger local probabilistic guarantees. This allows more direct analyses of the overall process, giving: Linear work parallel algorithms that construct spanners with O(k) stretch and size O(n1+1/k) in unweighted graphs, and size O(n1+1/k log k) in weighted graphs. Hopsets that lead to the first parallel algorithm for approximating shortest paths in undirected graphs with O(m poly log n) work.

Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods

In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring logarithmic factors involving the dimension of the input matrix and the size of its entries, both run in time \widetilde{O}(m\log \kappa \log^2 (1/≥ilon)) where ≥ilon is the amount of error we are willing to tolerate. Here, \kappa represents the ratio between the largest and the smallest entries of the optimal scalings. This implies that our algorithms run in nearly-linear time whenever \kappa is quasi-polynomial, which includes, in particular, the case of strictly positive matrices. We complement our results by providing a separate algorithm that uses an interior-point method and runs in time \widetilde{O}(m^{3/2} \log (1/≥ilon)).In order to establish these results, we develop a new second-order optimization framework that enables us to treat both problems in a unified and principled manner. This framework identifies a certain generalization of linear system solving that we can use to efficiently minimize a broad class of functions, which we call second-order robust. We then show that in the context of the specific functions capturing matrix scaling and balancing, we can leverage and generalize the work on Laplacian system solving to make the algorithms obtained via this framework very efficient.

Phenotypic Profiling Reveals that Candida albicans Opaque Cells Represent a Metabolically Specialized Cell State Compared to Default White Cells

ABSTRACT The white-opaque switch is a bistable, epigenetic transition affecting multiple traits in Candida albicans including mating, immunogenicity, and niche specificity. To compare how the two cell states respond to external cues, we examined the fitness, phenotypic switching, and filamentation properties of white cells and opaque cells under 1,440 different conditions at 25°C and 37°C. We demonstrate that white and opaque cells display striking differences in their integration of metabolic and thermal cues, so that the two states exhibit optimal fitness under distinct conditions. White cells were fitter than opaque cells under a wide range of environmental conditions, including growth at various pHs and in the presence of chemical stresses or antifungal drugs. This difference was exacerbated at 37°C, consistent with white cells being the default state of C. albicans in the mammalian host. In contrast, opaque cells showed greater fitness than white cells under select nutritional conditions, including growth on diverse peptides at 25°C. We further demonstrate that filamentation is significantly rewired between the two states, with white and opaque cells undergoing filamentous growth in response to distinct external cues. Genetic analysis was used to identify signaling pathways impacting the white-opaque transition both in vitro and in a murine model of commensal colonization, and three sugar sensing pathways are revealed as regulators of the switch. Together, these findings establish that white and opaque cells are programmed for differential integration of metabolic and thermal cues and that opaque cells represent a more metabolically specialized cell state than the default white state. IMPORTANCE Epigenetic transitions are an important mechanism by which microbes adapt to external stimuli. For Candida albicans, such transitions are crucial for adaptation to complex, fluctuating environments, and therefore contribute to its success as a human pathogen. The white-opaque switch modulates multiple C. albicans attributes, from sexual competency to niche specificity. Here, we demonstrate that metabolic circuits are extensively rewired between white and opaque states, so that the two cell types exhibit optimal fitness under different nutritional conditions and at different temperatures. We thereby establish that epigenetic events can profoundly alter the metabolism of fungal cells. We also demonstrate that epigenetic switching regulates filamentation and biofilm formation, two phenotypes closely associated with pathogenesis. These experiments reveal that white cells, considered the most clinically relevant form of C. albicans, are a “general-purpose” state suited to many environments, whereas opaque cells appear to represent a more metabolically specialized form of the species. Epigenetic transitions are an important mechanism by which microbes adapt to external stimuli. For Candida albicans, such transitions are crucial for adaptation to complex, fluctuating environments, and therefore contribute to its success as a human pathogen. The white-opaque switch modulates multiple C. albicans attributes, from sexual competency to niche specificity. Here, we demonstrate that metabolic circuits are extensively rewired between white and opaque states, so that the two cell types exhibit optimal fitness under different nutritional conditions and at different temperatures. We thereby establish that epigenetic events can profoundly alter the metabolism of fungal cells. We also demonstrate that epigenetic switching regulates filamentation and biofilm formation, two phenotypes closely associated with pathogenesis. These experiments reveal that white cells, considered the most clinically relevant form of C. albicans, are a “general-purpose” state suited to many environments, whereas opaque cells appear to represent a more metabolically specialized form of the species.

Negative-weight shortest paths and unit capacity minimum cost flow in Õ ( m 10/7 log W ) time: (extended abstract)

In this paper, we study a set of combinatorial optimization problems on weighted graphs: the shortest path problem with negative weights, the weighted perfect bipartite matching problem, the unit-capacity minimum-cost maximum flow problem, and the weighted perfect bipartite b-matching problem under the assumption that ||b||1 = O(m). We show that each of these four problems can be solved in O(m10/7 log W) time, where W is the absolute maximum weight of an edge in the graph, providing the first polynomial improvement in their sparse-graph time complexity in over 25 years. At a high level, our algorithms build on the interior-point method-based framework developed by Mądry (FOCS 2013) for solving unit-capacity maximum flow problem. We develop a refined way to analyze this framework, as well as provide new variants of the underlying preconditioning and perturbation techniques. Consequently, we are able to extend the whole interior-point method-based approach to make it applicable in the weighted graph regime.

Faster Algorithms for Computing the Stationary Distribution, Simulating Random Walks, and More

In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape probabilities. In particular, on a directed graph with n vertices and m edges, we show how to compute each quantity in time Õ(m3/4n + mn2/3), where the Õ notation suppresses polylog factors in n, the desired accuracy, and the appropriate condition number (i.e. the mixing time or restart probability). Our result improves upon the previous fastest running times for these problems; previous results either invoke a general purpose linear system solver on a n × n matrix with m nonzero entries, or depend polynomially on the desired error or natural condition number associated with the problem (i.e. the mixing time or restart probability). For sparse graphs, we obtain a running time of Õ(n7/4), breaking the O(n2) barrier of the best running time one could hope to achieve using fast matrix multiplication. We achieve our result by providing a similar running time improvement for solving directed Laplacian systems, a natural directed or asymmetric analog of the well studied symmetric or undirected Laplacian systems. We show how to solve such systems in time Õ(m3/4n + mn2/3), and efficiently reduce a broad range of problems to solving Õ(1) directed Laplacian systems on Eulerian graphs. We hope these results and our analysis open the door for further study into directed spectral graph theory.

Multidimensional Binary Search for Contextual Decision-Making

We consider a multidimensional search problem that is motivated by questions in contextual decision making, such as dynamic pricing and personalized medicine. Nature selects a state from a d-dimens...

How To Elect a Leader Faster than a Tournament

The problem of electing a leader from among n contenders is one of the fundamental questions in distributed computing. In its simplest formulation, the task is as follows: given n processors, all participants must eventually return a win or lose indication, such that a single contender may win. Despite a considerable amount of work on leader election, the following question is still open: can we elect a leader in an asynchronous fault-prone system faster than just running a Θ(log n)-time tournament, against a strong adaptive adversary? In this paper, we answer this question in the affirmative, improving on a decades-old upper bound. We introduce two new algorithmic ideas to reduce the time complexity of electing a leader to O( log* n), using O(n2) point-to-point messages. A non-trivial application of our algorithm is a new upper bound for the tight renaming problem, assigning n items to the n participants in expected O(log2 n ) time and O(n2) messages. We complement our results with lower bound of Ω(n2) messages for solving these two problems, closing the question of their message complexity.