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This paper focuses on space efficient representations of rooted trees that permit basic navigation in constant time. While most of the previous work has focused on binary trees, we turn our attention to trees of higher degree. We consider both cardinal trees (or k-ary tries), where each node has k slots, labelled {1,. .. , k}, each of which may have a… (More)

- Jonathan Bredin, Erik D. Demaine, Mohammad Taghi Hajiaghayi, Daniela Rus
- MobiHoc
- 2005

We consider the problem of deploying or repairing a sensor network to guarantee a specified level of multi-path connectivity (<i>k</i>-connectivity) between all nodes. Such a guarantee simultaneously provides fault tolerance against node failures and high capacity through multi-path routing. We design and analyze the first algorithms that place an… (More)

- Bodhi Priyantha, Hari Balakrishnan, Erik D. Demaine, Seth J. Teller
- SenSys
- 2003

Many sensor network applications require that each node's sensor stream be annotated with its physical location in some common coordinate system. Manual measurement and configuration methods for obtaining location don't scale and are error-prone, and equipping sensors with GPS is often expensive and does not work in indoor and urban deployments. Sensor… (More)

In the Order-Maintenance Problem, the objective is to maintain a total order subject to insertions, deletions, and precedence queries. Known optimal solutions, due to Dietz and Sleator, are complicated. We present new algorithms that match the bounds of Dietz and Sleator. Our solutions are simple, and we present experimental evidence that suggests that they… (More)

- Mihai Patrascu, Erik D. Demaine
- SODA
- 2004

We close the gaps between known lower and upper bounds for the online partial-sums problem in the RAM and group models of computation. If elements are chosen from an abstract group, we prove an Ω(lg <i>n</i>) lower bound on the number of algebraic operations that must be performed, matching a well-known upper bound. In the RAM model with <i>b</i>-bit… (More)

- Erik D. Demaine, Alejandro López-Ortiz, J. Ian Munro
- SODA
- 2000

Motivated by boolean queries in text database systems, we consider the problems of finding the intersection, union, or difference of a collection of sorted sets. While the worst-case complexity of these problems is straightforward , we consider a notion of complexity that depends on the particular instance. We develop the idea of a proof that a given set is… (More)

- Robert A. Hearn, Erik D. Demaine
- Theor. Comput. Sci.
- 2005

We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum inflow constraints on vertices. Deciding whether this simple graph model can be manipulated in order to reverse the direction of a particular edge is shown to be PSPACE-complete by a reduction from Quantified Boolean Formulas. We… (More)

We consider a router on the Internet analyzing the statistical properties of a TCP/IP packet stream. A fundamental difficulty with measuring traffic behavior on the Internet is that there is simply too much data to be recorded for later analysis, on the order of gigabytes a second. As a result, network routers can collect only relatively few statistics… (More)

- Bodhi Priyantha, Hari Balakrishnan, Erik D. Demaine, Seth J. Teller
- Proceedings IEEE 24th Annual Joint Conference of…
- 2005

The localization problem is to determine an assignment of coordinates to nodes in a wireless ad-hoc or sensor network that is consistent with measured pairwise node distances. Most previously proposed solutions to this problem assume that the nodes can obtain pairwise distances to other nearby nodes using some ranging technology. However, for a variety of… (More)