Elena Lodi

A preliminary study of a diagonal channel-routing model

The layout of two-terminal nets in a VLSI channel is realized in a new diagonal channel-routing model (DCRM), where the tracks are segments respectively displayed at +45 ° and −45 ° on the two layers of the channel. A new definition of channel density is introduced, and a lower bound to the channel width is derived by the application of an algorithm, whose complexity is evaluated as a function of the channel density, and other parameters of the problem.A simple linear-time algorithm is proposed, which produces an optimal layout (i.e., it requires a channel of minimum width) if the length of the longest net equals the lower bound for the channel width. In any case, the number of vias is at most one for each net. Some particular solutions are proposed for problems with long nets.Specific problems are much easier in DCRM than in the classical Manhattan model. For example, any shift-by-i can be realized in DCRM in a channel of widthi.

A 2 d channel router for the diagonal model

Abstract In this paper we consider two-terminal channel routing problems in a Diagonal Model (DM), where the grid consists of right and left tracks displayed at +45° and −45° on two layers. As in the Manhattan Model, the tracks are displaced in two layers with the left tracks on one layer and the right tracks on the other. InDM we prove a new lower bound to the channel width equal to d , and present an algorithm that obtains 2 d + 3 as an upper bound, where d is the channel density.

Dynamic monopolies in tori

Let G be a simple connected graph where every node is colored either black or white. Consider now the following repetitive process on G: each node recolors itself, at each local time step, with the color held by the majority of its neighbors. Depending on the initial assignment of colors to the nodes and on the definition of majority, different dynamics can occur. We are interested in dynamos; i.e., initial assignments of colors which lead the system to a monochromatic configuration in a finite number of steps. In the context of distributed computing and communication networks, this repetitive process is particularly important in that it describes the impact that a set of initial faults can have in majority-based systems (where black nodes correspond to faulty elements and white to non-faulty ones). In this paper, we study two particular forms of dynamos (irreversible and monotone) in tori, focusing on the minimum number of initial black elements needed to reach the fixed point. We derive lower and upper bounds on the size of dynamos for three types of tori, under different assumptions on the majority rule (simple and strong). These bounds are tight within an additive constant. The upper bounds are constructive: for each topology and each majority rule, we exhibit a dynamo of the claimed size.

Routing in times square mode

Abstract We propose a new channel routing model called times square mode (shortly TS , where the grid is composed of horizontal tracks , lines at +60° ( right tracks ), and lines at −60° ( left tracks ). In principle TS makes use of three layers, and can be seen as a variation of the classical Manhattan mode because each layer contains parallel tracks only. Restricting our attention to 2-terminal problems of density d , we present a simple polynomial routing algorithm for TS which produces a standard layout in a channel of width ⌜ 1 2 (d − 1)⌝ ⩽ w ⩽ 2d − 1 , or w ⩽ d + 1 for dense problems. We prove that this layout can be wired in three or four layers, and give a condition, testable in polynomial time, to decide the number of layers needed. Then we outline a wiring algorithm for three or four layers. Finally, we indicate how to extend our approach to multiterminal nets.

Irreversible Dynamos in Tori

We study the dynamics of majority-based distributed systems in presence of permanent faults. In particular, we are interested in the patterns of initial faults which may lead the entire system to a faulty behaviour. Such patterns are called dynamos and their properties have been studied in many different contexts. In this paper we investigate dynamos for meshes with different types of toroidal closures. For each topology we establish tight bounds on the number of faulty elements needed for a system break-down, under different majority rules.

A VLSI tree machine for relational data bases

A VLSI chip for performing relational data base operations is proposed. The chip is a tree of processors (TOP), where each chip has elementary storage and processing capabilities. A relation will be stored in the lowest levels of a TOP. More precisely, every m-tuple will occupy a subtree whose root is s&equil; [log2(m+1)] −1 levels above the leaves. Denoting by h the height of the tree, the upper h-s levels will be used for routing and bookkeeping purposes. A number of basic operations such as allocate and deallocate subtrees, insert and compare m-tuples etc., are defined for the TOPs. Relational operations are effectively performed as simple combinations of basic operations. The architecture of a data base machine based on TOPs is also sketched. Such a machine is feasible with the current VLSI technology and could become attractive in few years if density and performance of VLSI keep improving at the current rate.

Channel routing for strictly multiterminal nets

Abstract We define a strictly multiterminal (smt) channel routing problem (CRP) as one totally composed of smt-nets, that is nets with more than one entry terminal and more than one exit terminal. We show that any strictly multiterminal channel routing problem can be routed in a channel of height 3d in the Manhattan model (hence, in the knock-knee model), and of height 6d, or 6d + 2, in a diagonal model where d is the density of the CRP. The routing algorithm is also useful for general CRPs, if the number of smt-nets is predominant.

Minimum weight dynamo and fast opinion spreading

We consider the following multi---level opinion spreading model on networks. Initially, each node gets a weight from the set {0,…,k−1}, where such a weight stands for the individuals conviction of a new idea or product. Then, by proceeding to rounds, each node updates its weight according to the weights of its neighbors. We are interested in the initial assignments of weights leading each node to get the value k−1 ---e.g. unanimous maximum level acceptance--- within a given number of rounds. We determine lower bounds on the sum of the initial weights of the nodes under the irreversible simple majority rules, where a node increases its weight if and only if the majority of its neighbors have a weight that is higher than its own one. Moreover, we provide constructive tight upper bounds for some class of regular topologies: rings, tori, and cliques.

PARPST: a PARallel algorithm to find peptide sequence tags.

BackgroundProtein identification is one of the most challenging problems in proteomics. Tandem mass spectrometry provides an important tool to handle the protein identification problem.ResultsWe developed a work-efficient parallel algorithm for the peptide sequence tag problem. The algorithm runs on the concurrent-read, exclusive-write PRAM in O(n) time using log n processors, where n is the number of mass peaks in the spectrum. The algorithm is able to find all the sequence tags having score greater than a parameter or all the sequence tags of maximum length. Our tests on 1507 spectra in the Open Proteomics Database shown that our algorithm is efficient and effective since achieves comparable results to other methods.ConclusionsThe proposed algorithm can be used to speed up the database searching or to identify post-translational modifications, comparing the homology of the sequence tags found with the sequences in the biological database.

A parallel solution to the approximate string matching problem

The approximate string matching problem (ASMP) consists of finding all the occurrences of a string of characters X of length m in another string Y of length n, m<<n, where some errors are allowed in these occurrences. A classical sequential algorithm based on dynamic programming solves the problem in time of O(mn). A parallelisation scheme for this algorithm is proposed, which applies to a very general set of errors, and allows to solve ASMP in time T with N processors, with NT of O(mn), thereby achieving optimal speedup