Approximating Generalized Network Design under (Dis)economies of Scale with Applications to Energy Efficiency

In a generalized network design (GND) problem, a set of resources are assigned to multiple communication requests. Each request contributes its weight to the resources it uses and the total load on a resource is then translated to the cost it incurs via a resource specific cost function. For example, a request may be to establish a virtual circuit, thus contributing to the load on each edge in the circuit. Motivated by energy efficiency applications, recently, there is a growing interest in GND using cost functions that exhibit (dis)economies of scale ((D)oS), namely, cost functions that appear subadditive for small loads and superadditive for larger loads. The current paper advances the existing literature on approximation algorithms for GND problems with (D)oS cost functions in various aspects: (1) we present a generic approximation framework that yields approximation results for a much wider family of requests in both directed and undirected graphs; (2) our framework allows for unrelated weights, thus providing the first non-trivial approximation for the problem of scheduling unrelated parallel machines with (D)oS cost functions; (3) our framework is fully combinatorial and runs in strongly polynomial time; (4) the family of (D)oS cost functions considered in the current paper is more general than the one considered in the existing literature, providing a more accurate abstraction for practical energy conservation scenarios; and (5) we obtain the first approximation ratio for GND with (D)oS cost functions that depends only on the parameters of the resources' technology and does not grow with the number of resources, the number of requests, or their weights. The design of our framework relies heavily on Roughgarden's smoothness toolbox (JACM 2015), thus demonstrating the possible usefulness of this toolbox in the area of approximation algorithms.Comment: 39 pages, 1 figure. An extended abstract of this paper is to appear in the 50th Annual ACM Symposium on the Theory of Computing (STOC 2018

Bayesian Generalized Network Design

We study network coordination problems, as captured by the setting of generalized network design (Emek et al., STOC 2018), in the face of uncertainty resulting from partial information that the network users hold regarding the actions of their peers. This uncertainty is formalized using Alon et al.\u27s Bayesian ignorance framework (TCS 2012). While the approach of Alon et al. is purely combinatorial, the current paper takes into account computational considerations: Our main technical contribution is the development of (strongly) polynomial time algorithms for local decision making in the face of Bayesian uncertainty

Deterministic Leader Election in Programmable Matter

Addressing a fundamental problem in programmable matter, we present the first deterministic algorithm to elect a unique leader in a system of connected amoebots assuming only that amoebots are initially contracted. Previous algorithms either used randomization, made various assumptions (shapes with no holes, or known shared chirality), or elected several co-leaders in some cases. Some of the building blocks we introduce in constructing the algorithm are of interest by themselves, especially the procedure we present for reaching common chirality among the amoebots. Given the leader election and the chirality agreement building block, it is known that various tasks in programmable matter can be performed or improved. The main idea of the new algorithm is the usage of the ability of the amoebots to move, which previous leader election algorithms have not used

Composition Games for Distributed Systems: the EU Grant games (Abstract)

We analyze ways by which people decompose into groups in distributed systems. We are interested in systems in which an agent can increase its utility by connecting to other agents, but must also pay a cost that increases with the size of the sys- tem. The right balance is achieved by the right size group of agents. We formulate and analyze three intuitive and realistic games and show how simple changes in the protocol can dras- tically improve the price of anarchy of these games. In partic- ular, we identify two important properties for a low price of anarchy: agreement in joining the system, and the possibil- ity of appealing a rejection from a system. We show that the latter property is especially important if there are some pre- existing constraints regarding who may collaborate (or com- municate) with whom.Comment: Accepted at AAAI 2013: Twenty-Seventh Conference on Artificial Intelligence, Bellevue, Washington, US

Whole Genome Sequence Analysis of Mutations Accumulated in rad27Δ Yeast Strains with Defects in the Processing of Okazaki Fragments Indicates Template-Switching Events

Okazaki fragments that are formed during lagging strand DNA synthesis include an initiating primer consisting of both RNA and DNA. The RNA fragment must be removed before the fragments are joined. In Saccharomyces cerevisiae, a key player in this process is the structure-specific flap endonuclease, Rad27p (human homolog FEN1). To obtain a genomic view of the mutational consequence of loss of RAD27, a S. cerevisiae rad27Δ strain was subcultured for 25 generations and sequenced using Illumina paired-end sequencing. Out of the 455 changes observed in 10 colonies isolated the two most common types of events were insertions or deletions (INDELs) in simple sequence repeats (SSRs) and INDELs mediated by short direct repeats. Surprisingly, we also detected a previously neglected class of 21 template-switching events. These events were presumably generated by quasi-palindrome to palindrome correction, as well as palindrome elongation. The formation of these events is best explained by folding back of the stalled nascent strand and resumption of DNA synthesis using the same nascent strand as a template. Evidence of quasi-palindrome to palindrome correction that could be generated by template switching appears also in yeast genome evolution. Out of the 455 events, 55 events appeared in multiple isolates; further analysis indicates that these loci are mutational hotspots. Since Rad27 acts on the lagging strand when the leading strand should not contain any gaps, we propose a mechanism favoring intramolecular strand switching over an intermolecular mechanism. We note that our results open new ways of understanding template switching that occurs during genome instability and evolution