16166391
Linear k-arboricities on trees
Abstract For a fixed positive integer k, the linear k-arboricity lak(G) of a graph G is the minimum number l such that the edge set E(G) can be partitioned into l disjoint sets and that each induces a subgraph whose components are paths of lengths at most k. This paper studies linear k-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm to determine whether a tree T has lak(T)⩽m.
38200007
Total colorings of equibipartite graphs
Abstract The total chromatic number χτ ( G ) of a graph G is the least number of colors needed to color the vertices and the edges of G such that no adjacent or incident pair of elements receive the same color. A simple graph G is called type 1 if χτ ( G ) = Δ ( G ) + 1, where Δ ( G ) is the maximum degree of G . In this paper we prove the following conjecture of Chen et al.: An ( n − 2)-regular equibipartite graph K n , n − E ( J ) is type 1 if and only if J contains a 4-cycle.
5122226
Sensor networks for medical care
Sensor networks have the potential to greatly impact many aspects of medical care. By outfitting patients with wireless, wearable vital sign sensors, collecting detailed real-time data on physiological status can be greatly simplified. However, there is a significant gap between existing sensor network systems and the needs of medical care. In particular, medical sensor networks must support multicast routing topologies, node mobility, a wide range of data rates and high degrees of reliability, and security. This paper describes our experiences with developing a combined hardware and software platform for medical sensor networks, called CodeBlue. CodeBlue provides protocols for device discovery and publish/subscribe multihop routing, as well as a simple query interface that is tailored for medical monitoring. We have developed several medical sensors based on the popular MicaZ and Telos mote designs, including a pulse oximeter, EKG and motion-activity sensor. We also describe a new, miniaturized sensor mote designed for medical use. We present initial results for the CodeBlue prototype demonstrating the integration of our medical sensors with the publish/subscribe routing substrate. We have experimentally validated the prototype on our 30-node sensor network testbed, demonstrating its scalability and robustness as the number of simultaneous queries, data rates, and transmitting sensors are varied. We also study the effect of node mobility, fairness across multiple simultaneous paths, and patterns of packet loss, confirming the system’s ability to maintain stable routes despite variations in node location and
10767971
The duality between information embedding and source coding with side information and some applications
Aspects of the duality between the information-embedding problem and the Wyner-Ziv (1976) problem of source coding with side information at the decoder are developed and used to establish a spectrum new results on these and related problems, with implications for a number of important applications. The single-letter characterization of the information-embedding problem is developed and related to the corresponding characterization of the Wyner-Ziv problem, both of which correspond to optimization of a common mutual information difference. Dual variables and dual Markov conditions are identified, along with the dual role of noise and distortion in the two problems. For a Gaussian context with quadratic distortion metric, a geometric interpretation of the duality is developed. From such insights, we develop a capacity-achieving information-embedding system based on nested lattices. We show the resulting encoder-decoder has precisely the same decoder-encoder structure as the corresponding Wyner-Ziv system based on nested lattices that achieves the rate-distortion limit. For a binary context with Hamming distortion metric, the information-embedding capacity is developed, along with its relationship to the corresponding Wyner-Ziv rate-distortion function. In turn, an information-embedding system for this case based on nested linear codes is constructed having an encoder-decoder that is identical to the decoder-encoder structure for the corresponding system that achieves the Wyner-Ziv rate-distortion limit. Finally, based on these results, a simple layered joint source-channel coding system is developed with a perfectly symmetric encoder-decoder structure. Its application and performance is discussed in a broadcast setting in which there is a need to control the fidelity experienced by different receivers. Among other results, we show that such systems and their multilayer extensions retain attractive optimality properties in the Gaussian-quadratic case, but not in the binary-Hamming case.
694380
Automatic Fault Tree Derivation from Little-JIL Process Definitions
Defects in safety critical processes can lead to accidents that result in harm to people or damage to property. Therefore, it is important to find ways to detect and remove defects from such processes. Earlier work has shown that Fault Tree Analysis (FTA) [3] can be effective in detecting safety critical process defects. Unfortunately, it is difficult to build a comprehensive set of Fault Trees for a complex process, especially if this process is not completely well-defined. The Little-JIL process definition language has been shown to be effective for defining complex processes clearly and precisely at whatever level of granularity is desired [1]. In this work, we present an algorithm for generating Fault Trees from Little-JIL process definitions. We demonstrate the value of this work by showing how FTA can identify safety defects in the process from which the Fault Trees were automatically derived.
4000197
Lot-sizing scheduling with batch setup times
This paper is concerned with scheduling independent jobs on m parallel machines in such a way that the makespan is minimized. Each job j is allowed to split arbitrarily into several parts, which can be individually processed on any machine at any time. However, a setup for uninterrupted sj time units is required before any split part of job j can be processed on any machine. The problem is strongly NP-hard if the number m of machines is variable and weakly NP-hard otherwise. We give a polynomial-time $$\frac{5}{3}$$-approximation algorithm for the former case and a fully polynomial-time approximation scheme for the latter.
39846081
On-Line Algorithms for Cardinality Constrained Bin Packing Problems
The bin packing problem asks for a packing of a list of items from [0, 1] into the smallest possible number of bins having unit capacity. The k-item bin packing problem additionally imposes the constraint that at most k items are allowed in one bin. We present two efficient approximation algorithms for the on-line version of this problem. We show that, for increasing values of k, the asymptotic worst-case performance ratio of the first algorithm tends towards 2 and that the second algorithm has an asymptotic worst-case performance ratio of 2. Both heuristics considerably improve upon the best known result 2.7 of Krause, Shen and Schwetman. Moreover, we present algorithms for k = 2 and k = 3, where the result for k = 2 is best possible.