This report aims at a comprehensive survey of the literature dealing with the multicommodity flow problem. This problem arises naturally in network modelling wherever commodities, vehicles, or messages are to be shipped or transmitted from certain nodes of an underlying network to some others. Recent applications of mathematical programming techniques to traffic equilibrium problems in transportation studies as well as computer networks analysis has renewed considerable interest in this problem. This report discusses solution techniques for both linear and nonlinear flow problems. The former includes decomposition, partitioning, compact inverse methods, and primal-dual algorithms. Described is a variety of feasible direction methods for the latter. The report concludes by giving applications and computational experience for both types of problems.

Multicommodity network flows—A survey

We survey the problem of constructing the groups of a given finite order. We provide an extensive bibliography and outline practical algorithmic solutions to the problem. Motivated by the millennium, we used these methods to construct the groups of order at most 2000; we report on this calculation and describe the resulting group library.

A millennium project: constructing small groups

In a recent paper, Pierce studied the problems of communicating at optical frequencies using photon-counting techniques, and concluded that "at low temperatures we encounter insuperable problems of encoding long before we approach [channel capacity]." In this paper it is shown that even assuming a noiseless model for photon communication for which capacity (measured in nats/photon) is infinite, it is unlikely that a signaling efficiency of even 10 nats/photon could be achieved practically. On the positive side, it is shown that pulse-position modulation plus Reed-Solomon coding yields practical results in the range of 2 to 3 nats/photon.

/pdf/practical-codes-for-photon-communication-3d652baij1.pdf

Practical codes for photon communication

It is shown that When Pierce's pulse-position modulation scheme with 2Lpositions is used on a self-noise-limited directdetection optical communication channel, there results a 2L-ary erasure channel that is equivalent to the parallel combination of L "completely correlated" binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff rate of the full channel is shown to be much smaller than the sum of the cutoff rates. An interpretation of the cutoff rate is given that suggests a complexity advantage in coding separately on the component channels. It is shown that if short-constraint length convolutional codes with Viterbi decoders are used on the component channels, then the performance and complexity compare favorably with the Reed-Solomon coding system proposed by McEliece for the full channel. The reasons for this unexpectedly fine performance by the convolutional code system are explored in detail, as are various facets of the channel structure.

Capacity, Cutoff Rate, and Coding for a Direct-Detection Optical Channel

We develop two efficient procedures for generating cost allocation vectors in the core of a minimum cost spanning tree (m.c.s.t.) game. The first procedure requires O(n
 2) elementary operations to obtain each additional point in the core, wheren is the number of users. The efficiency of the second procedure, which is a natural strengthening of the first procedure, stems from the special structure of minimum excess coalitions in the core of an m.c.s.t. game. This special structure is later used (i) to ease the computational difficulty in computing the nucleolus of an m.c.s.t. game, and (ii) to provide a geometric characterization for the nucleolus of an m.c.s.t. game. This geometric characterization implies that in an m.c.s.t. game the nucleolus is the unique point in the intersection of the core and the kernel. We further develop an efficient procedure for generating fair cost allocations which, in some instances, coincide with the nucleolus. Finally, we show that by employing Sterns' transfer scheme we can generate a sequence of cost vectors which converges to the nucleolus.

On the core and nucleolus of minimum cost spanning tree games

We consider a model which is applicable to time-multi-plexed systems, such as multiplexed communication channels and time-shared computing facilities. In this (processor-sharing) queueing model, all jobs currently in the system share equally the processing capability of the server. In this paper, we investigate the processor-sharing model for the case of bulk arrivals. The mean response time of the system as a function of required service time is derived. An example is given to show the effect of bulk arrivals versus single arrivals for a constant utilization.

The processor-sharing queueing model for time-shared systems with bulk arrivals

An acoustic source generates an amplitude-modulated tone, with Doppler variations due to the relative motion between source andreceiver. A method is presented for real-time estimation of tone restfrequency and minimal distance between source and receiver, usingdigital signal processing techniques. The algorithm presented herewas implemented using a Texas Instruments TMS32010 processor.

Parameter Estimation Based on Doppler Frequency Shifts

Constantin and Rao [(1979), Inform. Contr. 40, 2036] have given an ingenious construction for a class of binary codes capable of correcting a single asymmetric error. In this paper we shall give a complete analysis of the size of these codes.

The constantinrao construction for binary asymmetric error-correcting codes

The groups of order 128

An analysis of the size of a class of binary codes capable of correcting a single asymmetric error is presented.

/pdf/the-constantin-rao-construction-for-binary-asymmetric-error-2plp7vo1w6.pdf

E. R. Rodemich

Papers

The processor-sharing queueing model for time-shared systems with bulk arrivals

Parameter Estimation Based on Doppler Frequency Shifts

The constantinrao construction for binary asymmetric error-correcting codes

The groups of order 128

The Constantin-Rao Construction for Binary Asymmetric Error-Correcting Codes