10630576
On cloud-antichains and related configurations
Abstract We introduce the concept of a cloud-antichain, which is a natural generalization of antichains in partially ordered sets, and solve some seemingly basic extrenal problems for them. Following the discovery of our identity (in[1]) we found the ‘missing term’, which converts Bollobas' inequality into an identity. It immediately yields the uniqueness in the Sperner Theorem for unrelated chains of subsets, which are an example of a cloud-antichain.
32850524
Linear inequalities for covering codes: Part I: Pair covering inequalities
The lower bounds on K(n,R), minimum number of codewords of any binary code of length n, and covering radius R are improved. A new technique combining the Hamming association scheme and the results of a classic problem of covering pairs by k-tuples is introduced. The new lower bounds are obtained by studying various linear inequalities satisfied by covering codes, and such an inequality is derived. The lower bounds for K(n,R) are studied for some special values of n and R, which serve as examples showing how the methods developed are applied to concrete cases. >
15006226
Bounds on the sizes of constant weight covering codes
Motivated by applications in universal data compression algorithms we study the problem of bounds on the sizes of constant weight covering codes. We are concerned with the minimal sizes of codes of lengthn and constant weightu such that every word of lengthn and weightv is within Hamming distanced from a codeword. In addition to a brief summary of part of the relevant literature, we also give new results on upper and lower bounds to these sizes. We pay particular attention to the asymptotic covering density of these codes. We include tables of the bounds on the sizes of these codes both for small values ofn and for the asymptotic behavior. A comparison with techniques for attaining bounds for packing codes is also given. Some new combinatorial questions are also arising from the techniques.
43476378
Partial converse for a relay channel
A special case of the general discrete memoryless relay channel is studied. This channel consists of an input x, a relay output z, a channel output y, and a noiseless channel of capacity C/sub r/ allowing the relay sender to send additional information to the decoder. The channel is described by a collection of distributions (p(y, z mod x)). The decoder uses the channel output y and a function f(z) of the relay output at a rate no greater than C/sub r/ to recover the message. Some results on the capacity of the channel are obtained. >
32960689
On Maximal Shadows of Members in Left-compressed Sets
Whereas Stanley, Proctor and others studied Sperner properties of the poset L(k,m) we consider shadows of left-compressed sets and derive asymptotic bounds on their sizes.
19004655
Identification via compressed data
A new coding problem is introduced for a correlated source (X/sup n/,Y/sup n/)/sub n=1//sup /spl infin//. The observer of X/sup n/ can transmit data depending on X/sup n/ at a prescribed rate R. Based on these data the observer of Y/sup n/ tries to identify whether for some distortion measure /spl rho/ (like the Hamming distance) n/sup -1/ /spl rho/(X/sup n/,Y/sup n/)/spl les/d, a prescribed fidelity criterion. We investigate as functions of R and d the exponents of two error probabilities, the probabilities for misacceptance, and the probabilities for misrejection. In the case where X/sup n/ and Y/sup n/ are independent, we completely characterize the achievable region for the rate R and the exponents of two error probabilities; in the case where X/sup n/ and Y/sup n/ are correlated, we get some interesting partial results for the achievable region. During the process, we develop a new method for proving converses, which is called "the inherently typical subset lemma". This new method goes considerably beyond the "entropy characterization" the "image size characterization," and its extensions. It is conceivable that this new method has a strong impact on multiuser information theory.
5888722
The transformation graph Gxyz when xyz=-++
The transformation graph G^-^+^+ of G is the graph with vertex set V(G)@?E(G) in which the vertex x and y are joined by an edge if one of the following conditions holds: (i) x,y@?V(G), and x and y are not adjacent in G, (ii) x,y@?E(G), and x and y are adjacent in G, (iii) one of x and y is in V(G) and the other is in E(G), and they are incident in G. In this paper, it is shown that for two graphs G and G^', G^-^+^+@?G^'^-^+^+ if and only if G@?G^'. Simple necessary and sufficient conditions are given for G^-^+^+ to be planar and hamiltonian, respectively. It is also shown that for a graph G, the edge-connectivity of G^-^+^+ is equal to its minimum degree. Two related conjectures and some research problems are presented.
19398479
An application of the AHP in 3PL vendor selection of a 4PL system
As a fourth party logistics provider integrates the capacities of third party logistics providers, 3PL vendor selection is an important problem. Furthermore, 3PL vendor selection is a complex multi-criteria decision problem. The decision made by the decision maker or an evaluation team can be improved by a systematic and logistical approach to access priorities based on the inputs of the decision maker or the team made by several people. The analytic hierarchy process (AHP) can be very useful in reaching a likely result which can satisfy the decision maker or the team. In this paper, an AHP-based model is formulated and applied to a case study to examining the function in 3PL vendor selection. The use of the proposed model indicates that the computed quantitative evaluations can be applied to improve the precision of the selection.
148323
Analysis of point-to-point packet delay in an operational network
In this paper we perform a detailed analysis of point-to-point packet delay in an operational tier-1 network. The point-to-point delay is the time between a packet entering a router in one PoP (an ingress point) and its leaving a router in another PoP (an egress point). It measures the one-way delay experienced by packets from an ingress point to an egress point across an ISP's network and provides the most basic information regarding the delay performance of the ISP's network. Using packet traces captured in the operational network, we obtain precise point-to-point packet delay measurements and analyze the various factors affecting them. Through a simple, step-by-step, systematic methodology and careful data analysis, we identify the major network factors that contribute to point-to-point packet delay and characterize their effect on the network delay performance. Our findings are: 1) delay distributions vary greatly in shape, depending on the path and link utilization; 2) after constant factors dependent only on the path and packet size are removed, the 99th percentile variable delay remains under 1 ms over several hops and under link utilization below 90% on a bottleneck; 3) a very small number of packets experience very large delay in short bursts
9330795
Application-specific instruction generation for configurable processor architectures
Designing an application-specific embedded system in nanometer technologies has become more difficult than ever due to the rapid increase in design complexity and manufacturing cost. Efficiency and flexibility must be carefully balanced to meet different application requirements. The recently emerged configurable and extensible processor architectures offer a favorable tradeoff between efficiency and flexibility, and a promising way to minimize certain important metrics (e.g., execution time, code size, etc.) of the embedded processors. This paper addresses the problem of generating the application-specific instructions to improve the execution speed for configurable processors. A set of algorithms, including pattern generation, pattern selection, and application mapping, are proposed to efficiently utilize the instruction set extensibility of the target configurable processor. Applications of our approach to several real-life benchmarks on the Altera Nios processor show encouraging performance speedup (2.75X on average and up to 3.73X in some cases).
3006898
A six-color theorem for the edge-face coloring of plane graphs
Abstract It was shown (Kronk and Mitchen, 1973) that the set of vertices, edges and faces of any normal map on the sphere can be colored with seven colors. In this paper we solve a somewhat different problem: the set of edges and faces of any plane graph with Δ ⩽ 3 can be colored by six colors.