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We give the rst non-trivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work were the trivial O(k)-approximations. For the directed Steiner(More)
Recently Rothemund and Winfree [6] have considered the program size complexity of constructing squares by self-assembly. Here, we consider the time complexity of such constructions using a natural generalization of the Tile Assembly Model defined in [6]. In the generalized model, the Rothemund-Winfree construction of <italic>n \times n</italic> squares(More)
Distributed hash table (DHT) systems are an important class of peer-to-peer routing infrastructures. They enable scalable wide-area storage and retrieval of information, and will support the rapid development of a wide variety of Internet-scale applications ranging from naming systems and file systems to application-layer multicast. DHT systems essentially(More)
— The Internet is facing two problems simultaneously: there is a need for a faster switching/routing infrastructure, and a need to introduce guaranteed qualities of service (QoS). Each problem can be solved independently: switches and routers can be made faster by using input-queued crossbars, instead of shared memory systems; and QoS can be provided using(More)
Wireless sensor networks (WSNs) are emerging as an effective means for environment monitoring. This paper investigates a strategy for energy efficient monitoring in WSNs that partitions the sensors into covers, and then activates the covers iteratively in a round-robin fashion. This approach takes advantage of the overlap created when many sensors monitor a(More)
WTF ("Who to Follow") is Twitter's user recommendation service, which is responsible for creating millions of connections daily between users based on shared interests, common connections, and other related factors. This paper provides an architectural overview and shares lessons we learned in building and running the service over the past few years.(More)
Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to(More)
Most optimization problems on an undirected graph reduce in complexity when restricted to instances on a t.ree. A recent result [3] for probabiistically approsimating graph metrics by trees such that no edge &retches (in an expected sense) by more than a factor of O(log2 n) has resulted in several approximation algorithms which exploit the ease of solving(More)