[Show abstract][Hide abstract] ABSTRACT: Understanding the dynamics of evolving social or infrastructure networks is a
challenge in applied areas such as epidemiology, viral marketing, or urban
planning. During the past decade, data has been collected on such networks but
has yet to be fully analyzed. We propose to use information on the dynamics of
the data to find stable partitions of the network into groups. For that
purpose, we introduce a time-dependent, dynamic version of the facility
location problem, that includes a switching cost when a client's assignment
changes from one facility to another. This might provide a better
representation of an evolving network, emphasizing the abrupt change of
relationships between subjects rather than the continuous evolution of the
underlying network. We show that in realistic examples this model yields indeed
better fitting solutions than optimizing every snapshot independently. We
present an $O(\log nT)$-approximation algorithm and a matching hardness result,
where $n$ is the number of clients and $T$ the number of time steps. We also
give an other algorithms with approximation ratio $O(\log nT)$ for the variant
where one pays at each time step (leasing) for each open facility.
[Show abstract][Hide abstract] ABSTRACT: We give simple linear-time algorithms for two problems in planar graphs: max st-flow in directed graphs with unit capacities, and multiple-source shortest paths in undirected graphs with unit lengths.
Proceedings of the forty-fifth annual ACM symposium on Theory of computing; 06/2013
[Show abstract][Hide abstract] ABSTRACT: Recent years have seen the development of several different systems for software transactional memory (STM). Most either employ locks in the underlying implementation or depend on thread-safe general-purpose garbage collection to collect stale data and metadata. We consider the design of low-overhead, obstruction-free software transactional memory for non-garbage-collected languages. Our design eliminates dynamic allocation of transactional meta-data and co-locates data that are separate in other systems, thereby reducing the expected number of cache misses on the common-case code path, while preserving nonblocking progress and requiring no atomic instructions other than single-word load, store, and compare-and-swap (or load-linked/store-conditional). We also employ a simple, epoch-based storage management system and introduce a novel conservative mechanism to make reader transactions visible to writers without inducing additional metadata copying or dynamic allocation. Experimental results show throughput significantly higher than that of existing nonblocking STM systems, and highlight significant application-specific differences among conflict detection and validation strategies.
[Show abstract][Hide abstract] ABSTRACT: We give an $O(n \log^3 n)$ approximation scheme for Steiner forest in planar
graphs, improving on the previous approximation scheme for this problem, which
runs in $O(n^{f(\epsilon)})$ time.
[Show abstract][Hide abstract] ABSTRACT: Abstract We show that random DNF formulas, random log-depth decision trees and random determin- istic finite acceptors cannot be weakly learned with a polynomial number of statistical queries with respect to an arbitrary distribution.
Algorithmic Learning Theory, 21st International Conference, ALT 2010, Canberra, Australia, October 6-8, 2010. Proceedings; 12/2010
[Show abstract][Hide abstract] ABSTRACT: We consider the question of how much information can be stored by labeling the vertices of a connected undirected graph G using a constant-size set of labels, when isomorphic labelings are not distinguishable. An exact information-theoretic bound
is easily obtained by counting the number of isomorphism classes of labelings of G, which we call the information-theoretic capacity of the graph. More interesting is the effective capacity of members of some class of graphs, the number of states distinguishable by a Turing machine that uses the labeled graph
itself in place of the usual linear tape. We show that the effective capacity equals the information-theoretic capacity up
to constant factors for trees, random graphs with polynomial edge probabilities, and bounded-degree graphs.
Stabilization, Safety, and Security of Distributed Systems - 12th International Symposium, SSS 2010, New York, NY, USA, September 20-22, 2010. Proceedings; 12/2010
[Show abstract][Hide abstract] ABSTRACT: What does a typical road network look like? Existing generative models tend
to focus on one aspect to the exclusion of others. We introduce the
general-purpose \emph{quadtree model} and analyze its shortest paths and
maximum flow.
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of minimizing contention in static dictionary data structures, where the contention on each cell is measured by the expected number of probes to that cell given an input that is chosen from a distribution that is not known to the query algorithm (but that may be known when the data structure is built). When all positive queries are equally probable, and similarly all negative queries are equally probable, we show that it is possible to construct a data structure using linear space s, a constant number of queries, and with contention O(1/s) on each cell, corresponding to a nearly-flat load distribution. All of these quantities are asymptotically optimal. For arbitrary query distributions, the lack of knowledge of the query distribution by the query algorithm prevents perfect load leveling in this case: we present a lower bound, based on VC-dimension, that shows that for a wide range of data structure problems, achieving contention even within a polylogarithmic factor of optimal requires a cell-probe complexity of Ω(log log n).
SPAA 2010: Proceedings of the 22nd Annual ACM Symposium on Parallelism in Algorithms and Architectures, Thira, Santorini, Greece, June 13-15, 2010; 06/2010
[Show abstract][Hide abstract] ABSTRACT: We show that 2 is the minimum VC dimension of a concept class whose k-fold union has VC dimension Ω(klogk)Ω(klogk).
Information Processing Letters 11/2009; 109(23-24):1232-1234. DOI:10.1016/j.ipl.2009.09.005 · 0.55 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We describe and analyze a 3-state one-way population protocol to compute approximate majority in the model in which pairs
of agents are drawn uniformly at random to interact. Given an initial configuration of x’s, y’s and blanks that contains at least one non-blank, the goal is for the agents to reach consensus on one of the values x or y. Additionally, the value chosen should be the majority non-blank initial value, provided it exceeds the minority by a sufficient
margin. We prove that with high probability n agents reach consensus in O(n log n) interactions and the value chosen is the majority provided that its initial margin is at least w(Ön logn){\omega(\sqrt{n} \,{\rm log}\, n)}. This protocol has the additional property of tolerating Byzantine behavior in o(Ön){o(\sqrt{n})} of the agents, making it the first known population protocol that tolerates Byzantine agents.
[Show abstract][Hide abstract] ABSTRACT: The question of whether all shared objects with consensus number 2 belong to Common2, the set of objects that can be implemented in a wait-free manner by any type of consensus number 2, was first posed by Herlihy. In the absence of general results, several researchers have obtained implementations for restricted-concurrency versions of FIFO queues. We present the first Common2 algorithm for a queue with two enqueuers and any number of dequeuers.
[Show abstract][Hide abstract] ABSTRACT: For a rooted graph G, let EVb(G;p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We determine the expected value of EVb(G;p) for random trees, and include a connection to unrooted trees. We also consider rooted digraphs, computing the expected value of a random orientation of a rooted graph G in terms of EVb(G;p). We consider optimal location of the root vertex for the class of grid graphs, and we also briefly discuss a polynomial that incorporates vertex failure.
[Show abstract][Hide abstract] ABSTRACT: For a rooted graph G, let EV (G;p) be the expected number of ver- tices reachable from the root when each edge has an independent probability p of operating successfully. We examine combinatorial properties of this polyno- mial, proving that G is k-edge connected i EV 0(G;1) = ··· = EV k 1(G;1) = 0. We find bounds on the first and second derivatives of EV (G;p); applications yield characterizations of rooted paths and cycles in terms of the polynomial. We prove reconstruction results for rooted trees and a negative result con- cerning reconstruction of more complicated rooted graphs. We conclude by proving the norm of the largest root of EV (G;p) in Q(i) gives a sharp lower bound on the number of vertices of G.
[Show abstract][Hide abstract] ABSTRACT: We define a model of learning probabilistic acyclic circuits using value injection queries, in which an arbitrary subset of wires is set to fixed values, and the value on the single output wire is observed. We adapt the approach of using test paths from the Circuit Builder algorithm (AACW06) to show that there is a polynomial time algorithm that uses valueinjectionqueriestolearnBooleanprobabilis- tic circuits of constant fan-in and log depth. In the process, we discover that test paths fail utterly for circuits over alphabets of size greater than two and establish upper and lower bounds on the atten- uation factor for general and transitively reduced Boolean probabilistic circuits of test paths versus general experiments. To overcome the limitations of test paths for non-Boolean alphabets, we intro- duce function injection queries, which allow the symbols on a wire to be mapped to other symbols rather than just to themselves or constants.
21st Annual Conference on Learning Theory - COLT 2008, Helsinki, Finland, July 9-12, 2008; 01/2008
[Show abstract][Hide abstract] ABSTRACT: We describe and analyze a 3-state one-way population protocol for approximate majority in the model in which pairs of agents
are drawn uniformly at random to interact. Given an initial configuration of x’s, y’s and blanks that contains at least one non-blank, the goal is for the agents to reach consensus on one of the values x or y. Additionally, the value chosen should be the majority non-blank initial value, provided it exceeds the minority by a sufficient
margin. We prove that with high probability n agents reach consensus in O(n logn) interactions and the value chosen is the majority provided that its initial margin is at least
w(Ö{n logn})\omega(\sqrt{n \log n})
. This protocol has the additional property of tolerating Byzantine behavior in
o(Ön)o(\sqrt{n})
of the agents, making it the first known population protocol that tolerates Byzantine agents. Turning to the register machine
construction from[2], we apply the 3-state approximate majority protocol and other techniques to speed up the per-step parallel
time overhead of the simulation from O(log4
n) to O(log2
n). To increase the robustness of the phase clock at the heart of the register machine, we describe a consensus version of
the phase clock and present encouraging simulation results; its analysis remains an open problem.
[Show abstract][Hide abstract] ABSTRACT: The known O(dklogk) bound on the VC dimension of k-fold unions or intersections of a given concept class with VC dimension d is shown to be asymptotically tight.
Information Processing Letters 03/2007; 101(5):181-184. DOI:10.1016/j.ipl.2006.10.004 · 0.55 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Fast algorithms are presented for performing computations in a probabilistic population model. This is a variant of the standard
population protocol model—in which finite-state agents interact in pairs under the control of an adversary scheduler—where
all pairs are equally likely to be chosen for each interaction. It is shown that when a unique leader agent is provided in
the initial population, the population can simulate a virtual register machine in which standard arithmetic operations like
comparison, addition, subtraction, and multiplication and division by constants can be simulated in O(n log4
n) interactions with high probability. Applications include a reduction of the cost of computing a semilinear predicate to
O(n log4
n) interactions from the previously best-known bound of O(n
2 logn) interactions and simulation of a LOGSPACE Turing machine using the same O(n log4
n) interactions per step. These bounds on interactions translate into O(log4
n) time per step in a natural parallel model in which each agent participates in an expected Θ(1) interactions per time unit.
The central method is the extensive use of epidemics to propagate information from and to the leader, combined with an epidemic-based
phase clock used to detect when these epidemics are likely to be complete.
[Show abstract][Hide abstract] ABSTRACT: We consider the model of population protocols introduced by Angluin et al., in which anonymous finite-state agents stably compute a predicate of the multiset of their inputs via two-way interactions in the all-pairs family of communication networks. We prove that all predicates stably computable in this model (and certain generalizations of it) are semilinear, answering a central open question about the power of the model. Removing the assumption of two-way interaction, we also consider several variants of the model in which agents communicate by anonymous message-passing where the recipient of each message is chosen by an adversary and the sender is not identified to the recipient. These one-way models are distinguished by whether messages are delivered immediately or after a delay, whether a sender can record that it has sent a message, and whether a recipient can queue incoming messages, refusing to accept new messages until it has had a chance to send out messages of its own. We characterize the classes of predicates stably computable in each of these one-way models using natural subclasses of the semilinear predicates.
[Show abstract][Hide abstract] ABSTRACT: The greedoid Tutte polynomial of a tree is equivalent to a generating function that encodes information about the number of subtrees with II internal (non-leaf) edges and LL leaf edges, for all I and L. We prove that this information does not uniquely determine the tree T by constructing an infinite family of pairs of non-isomorphic caterpillars, each pair having identical subtree data. This disproves conjectures of [S. Chaudhary, G. Gordon, Tutte polynomials for trees, J. Graph Theory 15 (1991) 317–331] and [G. Gordon, E. McDonnell, D. Orloff, N. Yung, On the Tutte polynomial of a tree, Congr. Numer. 108 (1995) 141–151] and contrasts with the situation for rooted trees, where this data completely determines the rooted tree.