A Modified Decomposition Algorithm for Maximum Weight Bipartite Matching and Its Experimental Evaluation

Let G be an undirected bipartite graph with positive integer weights on the edges. We refine the existing decomposition theorem originally proposed by Kao et al., for computing maximum weight bipartite matching. We apply it to design an efficient version of the decomposition algorithm to compute the weight of a maximum weight bipartite matching of G in O(|V |W /k(|V |, W /N))-time by employing an algorithm designed by Feder and Motwani as a subroutine, where |V | and N denote the number of nodes and the maximum edge weight of G, respectively and k(x, y) = log x/ log(x 2 /y). The parameter W is smaller than the total edge weight W, essentially when the largest edge weight differs by more than one from the second largest edge weight in the current working graph in any decomposition step of the algorithm. In best case W = O(|E|) where |E| be the number of edges of G and in worst case W = W, that is, |E| ≤ W ≤ W. In addition, we talk about a scaling property of the algorithm and research a better bound of the parameter W. An experimental evaluation on randomly generated data shows that the proposed improvement is significant in general

Two-Dimensional Z-Complementary Array Quads with Low Column Sequence PMEPRs

In this paper, we first propose a new design strategy of 2D $Z$-complementary array quads (2D-ZCAQs) with feasible array sizes. A 2D-ZCAQ consists of four distinct unimodular arrays satisfying zero 2D auto-correlation sums for non-trivial 2D time-shifts within certain zone. Then, we obtain the upper bounds on the column sequence peak-to-mean envelope power ratio (PMEPR) of the constructed 2D-ZCAQs by using specific auto-correlation properties of some seed sequences. The constructed 2D-ZCAQs with bounded column sequence PMEPR can be used as a potential alternative to 2D Golay complementary array sets for practical applicationsComment: This work has been presented in 2023 IEEE International Symposium on Information Theory (ISIT), Taipei, Taiwa

Root Cross Z-Complementary Pairs with Large ZCZ Width

In this paper, we present a new family of cross $Z$-complementary pairs (CZCPs) based on generalized Boolean functions and two roots of unity. Our key idea is to consider an arbitrary partition of the set $\{1,2,\cdots, n\}$ with two subsets corresponding to two given roots of unity for which two truncated sequences of new alphabet size determined by the two roots of unity are obtained. We show that these two truncated sequences form a new $q$-ary CZCP with flexible sequence length and large zero-correlation zone width. Furthermore, we derive an enumeration formula by considering the Stirling number of the second kind for the partitions and show that the number of constructed CZCPs increases significantly compared to the existing works.Comment: This work has been presented in 2022 IEEE International Symposium on Information Theory (ISIT), Espoo, Finlan

On DNA Codes Over the Non-Chain Ring Z4+uZ4+u2Z4\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4 with u3=1u^3=1

In this paper, we present a novel design strategy of DNA codes with length $3n$ over the non-chain ring $R=\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$ with $64$ elements and $u^3=1$, where $n$ denotes the length of a code over $R$. We first study and analyze a distance conserving map defined over the ring $R$ into the length-$3$ DNA sequences. Then, we derive some conditions on the generator matrix of a linear code over $R$, which leads to a DNA code with reversible, reversible-complement, homopolymer $2$-run-length, and $\frac{w}{3n}$-GC-content constraints for integer $w$ ($0\leq w\leq 3n$). Finally, we propose a new construction of DNA codes using Reed-Muller type generator matrices. This allows us to obtain DNA codes with reversible, reversible-complement, homopolymer $2$-run-length, and $\frac{2}{3}$-GC-content constraints.Comment: This paper has been presented in IEEE Information Theory Workshop (ITW) 2022, Mumbai, INDI

Near-Optimal Zero Correlation Zone Sequence Sets from Paraunitary Matrices

Zero correlation zone (ZCZ) sequence sets play an important role in interference-free quasi-synchronous code-division multiple access communications. In this paper, for the first time, we investigate the periodic correlation properties of polyphase sequences obtained from paraunitary (PU) matrices, which shows the inherent relationship between PU matrix and ZCZ sequence sets. Our investigation suggests that any arbitrary PU matrix can produce ZCZ sequence sets by controlling its expanded form. The key idea is to impose certain restrictions on the expanded forms of the PU matrices to enable precise computation of the periodic correlation functions of the constructed sequences. We show that our proposed construction leads to near-optimal ZCZ sequence sets with regard to the ZCZ set size upper bound

Construction of New Optimal Z-Complementary Code Sets from Z-Paraunitary Matrices

In this paper, we first introduce a novel concept, called Z-paraunitary (ZPU) matrices. These ZPU matrices include conventional PU matrices as a special case. Then, we show that there exists an equivalence between a ZPU matrix and a Z-complementary code set (ZCCS) when the latter is expressed as a matrix with polynomial entries. The proposed ZPU matrix has an advantage over the conventional PU matrix with regard to the availability of wider range of matrix sizes and sequence lengths. In addition, the proposed construction framework can accommodate more choices of ZCCS parameters compared to the existing works

Cadmium in the purpleback flying squid Sthenoteuthis oualaniensis (Lesson, 1830) along northwest coast of India

The purpleback flying squid Sthenoteuthis oualaniensis (Lesson, 1830) is landed in small quantities along the northwest coast of India. Keeping in view the possibility of utilization of this species for domestic and export markets, the cadmium accumulation in the body tissues, which often causes concern, was studied. The dorsal mantle length of male and female observed during the study ranged from 34 to 47 cm and 30 to 32 cm respectively. The highest mean concentration of 435.22 ± 61.27 μg g-1 (mean ± S.E.) of Cd was found in the liver. Accumulation of Cd was also prominent in the gut, gills and skin. Moderate concentration of Cd (1 to 4 μg g-1) was observed in the nidamental gland, accessory nidamental gland, eyes, tentacles and muscle. In the gonads and arms, the concentration was below the acceptability level of 1.0 μg g-1. Higher accumulation in most of the organs/tissues of larger squids was observed. Significantly higher accumulation (p < 0.05) was noticed in the liver of larger specimens, indicating bioaccumulation. As the mean Cd content in the edible part was more than 1.0 μg g-1, this study highlights the need for detailed investigations to understand the bioaccumulation of Cd in Sthenoteuthis oualaniensi