Jared Saia

A framework for analysis of dynamic social networks

Finding patterns of social interaction within a population has wide-ranging applications including: disease modeling, cultural and information transmission, and behavioral ecology. Social interactions are often modeled with networks. A key characteristic of social interactions is their continual change. However, most past analyses of social networks are essentially static in that all information about the time that social interactions take place is discarded. In this paper, we propose a new mathematical and computational framework that enables analysis of dynamic social networks and that explicitly makes use of information about when social interactions occur.

Dynamically Fault-Tolerant Content Addressable Networks

We describe a content addressable network which is robust in the face of massive adversarial attacks and in a highly dynamic environment. Our network is robust in the sense that at any time, an arbitrarily large fraction of the peers can reach an arbitrarily large fraction of the data items. The network can be created and maintained in a completely distributed fashion.

Choosing a random peer

We present the first fully distributed algorithm which chooses a peer uniformly at random from the set of all peers in a distributed hash table (DHT). Our algorithm has latency O(log n) and sends O(log n) messages in expectation for a DHT like Chord [17]. Our motivation for studying this problem is threefold: to enable data collection by statistically rigorous sampling methods; to provide support for randomized, distributed algorithms over peer-to-peer networks; and to support the creation and maintenance of random links, and thereby offer a simple means of improving fault-tolerance.

Making chord robust to byzantine attacks

Chord is a distributed hash table (DHT) that requires only O(log n) links per node and performs searches with latency and message cost O(log n), where n is the number of peers in the network. Chord assumes all nodes behave according to protocol. We give a variant of Chord which is robust with high probability for any time period during which: 1) there are always at least z total peers in the network for some integer z; 2) there are never more than (1/4–e)z Byzantine peers in the network for a fixed e > 0; and 3) the number of peer insertion and deletion events is no more than zk for some tunable parameter k. We assume there is an adversary controlling the Byzantine peers and that the IP-addresses of all the Byzantine peers and the locations where they join the network are carefully selected by this adversary. Our notion of robustness is rather strong in that we not only guarantee that searches can be performed but also that we can enforce any set of “proper behavior” such as contributing new material, etc. In comparison to Chord, the resources required by this new variant are only a polylogarithmic factor greater in communication, messaging, and linking costs.

An Experimental Study of Data Migration Algorithms

The data migration problem is the problem ofc omputing a plan for moving data objects stored on devices in a network from one configuration to another. Load balancing or changing usage patterns might necessitate such a rearrangement ofda ta. In this paper, we consider the case where the objects are fixed-size and the network is complete. We introduce two new data migration algorithms, one ofwh ich has provably good bounds. We empirically compare the performance of these new algorithms against similar algorithms from Hall et al. [7] which have better theoretical guarantees and find that in almost all cases, the new algorithms perform better. We also find that both the new algorithms and the ones from Hall et al. perform much better in practice than the theoretical bounds suggest.

Finding spread blockers in dynamic networks

Social interactions are conduits for various processes spreading through a population, from rumors and opinions to behaviors and diseases. In the context of the spread of a disease or undesirable behavior, it is important to identify blockers: individuals that are most effective in stopping or slowing down the spread of a process through the population. This problem has so far resisted systematic algorithmic solutions. In an effort to formulate practical solutions, in this paper we ask: Are there structural network measures that are indicative of the best blockers in dynamic social networks? Our contribution is two-fold. First, we extend standard structural network measures to dynamic networks. Second, we compare the blocking ability of individuals in the order of ranking by the new dynamic measures. We found that overall, simple ranking according to a nodes static degree, or the dynamic version of a nodes degree, performed consistently well. Surprisingly the dynamic clustering coefficient seems to be a good indicator, while its static version performs worse than the random ranking. This provides simple practical and locally computable algorithms for identifying key blockers in a network.

Breaking the O ( n 2 ) bit barrier: scalable byzantine agreement with an adaptive adversary

We describe an algorithm for Byzantine agreement that is scalable in the sense that each processor sends only Õ(√n) bits, where n is the total number of processors. Our algorithm succeeds with high probability against an adaptive adversary, which can take over processors at any time during the protocol, up to the point of taking over arbitrarily close to a 1/3 fraction. We assume synchronous communication but a rushing adversary. Moreover, our algorithm works in the presence of flooding: processors controlled by the adversary can send out any number of messages. We assume the existence of private channels between all pairs of processors but make no other cryptographic assumptions. Finally, our algorithm has latency that is polylogarithmic in n. To the best of our knowledge, ours is the first algorithm to solve Byzantine agreement against an adaptive adversary, while requiring o(n2) total bits of communication.

Scalable leader election

In the leader election problem, there are n processors of which (1 - b)n are good. The problem is to design a distributed protocol to elect a good leader from the set of all processors. In this paper, we present a scalable leader election protocol. Our protocol is scalable in the sense that each good processor sends and processes a number of bits which is only polylogarithmic in n. (We assume no limit on the number of messages sent by bad processors.) For b < 1/3, our protocol elects a good leader with constant probability and ensures that a 1 - o(1) fraction of the good processors know this leader.We assume a point-to-point full information model. This is similar to the full information model, but harder in the sense that in a given round, a bad processor may send different messages to different processors, rather than having to broadcast the same message to every processor.To the best of our knowledge, we present the first leader election protocol that ensures that each good processor sends and processes a sublinear number of bits. Having reduced the problem of leader election to one of informing all good processors of a bit held by 1 − o(1) fraction of good processors, we conjecture that the solution to this problem is not possible within polylogarithmic message bounds.Our techniques can be used to provide scalable solutions to Byzantine agreement and other problems.

Discrete sensor placement problems in distribution networks

We consider the problem of placing sensors in a network to detect and identify thesource of any contamination. We consider two variants of this problem:0(1)sensor-constrained: we are allowed a fixed number of sensors and want to minimize contaminationdetection time; and (2)time-constrained: we must detect contamination within a given time limit and want to minimize the number of sensors required. Our main results are as follows. First, we give a necessary and sufficient condition for source identification.Second, we show that the sensor and time constrained versions of the problem are polynomially equivalent. Finally, we show that the sensor-constrained version of the problem is polynomially equivalent to the asymmetric k-center problem and that the time-constrained version of the problem is polynomially equivalent to the dominating set problem.

Single valued combinatorial auctions with budgets

We consider budget constrained combinatorial auctions where each bidder has a private value for each of the items in some subset of the items and an overall budget constraint. Such auctions capture adword auctions, where advertisers offer a bid for those adwords that (hopefully) target their intended audience, and advertisers also have budgets. It is known that even if all items are identical and all budgets are public it is not possible to be truthful and efficient. Our main result is a novel auction that runs in polynomial time, is incentive compatible, and ensures Pareto-optimality. The auction is incentive compatible with respect to the private valuations whereas the budgets and the sets of interest are assumed to be public knowledge. This extends the result of Dobzinski, Lavi and Nisan (FOCS 2008) for auctions of multiple identical items with bugets to single-valued combinatorial auctions and address one of the basic challenges on auctioning web ads (see Nisan et al, 2009, Google auctions for tv ads).