Parameterized Complexity of Path Set Packing

In PATH SET PACKING, the input is an undirected graph $G$, a collection $\cal P$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\cal P$. We study the parameterized complexity of PATH SET PACKING with respect to both natural and structural parameters. We show that the problem is $W[1]$-hard with respect to vertex cover plus the maximum length of a path in $\cal P$, and $W[1]$-hard respect to pathwidth plus maximum degree plus solution size. These results answer an open question raised in COCOON 2018. On the positive side, we show an FPT algorithm parameterized by feedback vertex set plus maximum degree, and also show an FPT algorithm parameterized by treewidth plus maximum degree plus maximum length of a path in $\cal P$. Both the positive results complement the hardness of PATH SET PACKING with respect to any subset of the parameters used in the FPT algorithms

An FPT algorithm for Matching Cut and d-cut

Given a positive integer $d$, the $d$-CUT problem is to decide if an undirected graph $G=(V,E)$ has a non trivial bipartition $(A,B)$ of $V$ such that every vertex in $A$ (resp. $B$) has at most $d$ neighbors in $B$ (resp. $A$). When $d=1$, this is the MATCHING CUT problem. Gomes and Sau, in IPEC 2019, gave the first fixed parameter tractable algorithm for $d$-CUT, when parameterized by maximum number of the crossing edges in the cut (i.e. the size of edge cut). However, their paper doesn't provide an explicit bound on the running time, as it indirectly relies on a MSOL formulation and Courcelle's Theorem. Motivated by this, we design and present an FPT algorithm for the MATCHING CUT (and more generally for $d$-CUT) for general graphs with running time $2^{O(k\log k)}n^{O(1)}$ where $k$ is the maximum size of the edge cut. This is the first FPT algorithm for the MATCHING CUT (and $d$-CUT) with an explicit dependence on this parameter. We also observe a lower bound of $2^{\Omega(k)}n^{O(1)}$ with same parameter for MATCHING CUT assuming ETH

Reversal of Glanzmann thrombasthenia platelet phenotype after imatinib treatment in a pediatric chronic myeloid leukemia patient

Chronic Myelogenous Leukemia (CML) is a myeloproliferative neoplasm characterized by proliferation of Philadelphia positive clonal pluripotent hematopoietic cells. Bleeding is a rare presentation of CML that can occur due to platelet dysfunction. Both pre-treatment and post-treatment platelet function abnormalities in CML have been described in the literature. We describe a rare case of childhood CML who presented with mucocutateous bleeding manifestations. On laboratory workup, a Glanzmann Thrombasthenia (GT) like platelet phenotype was demonstrated along with confirmation of diagnosis of CML in chronic phase. The acquired nature of platelet function defect was confirmed by demonstrating recovery of platelet antigens glycoprotein IIb/IIIa after achieving complete hematological response with Imatinib. Due to presenting complaint of bleeding diathesis and absence of hepatosplenomegaly, the case was undiagnosed for CML until the patient reported to us. Careful evaluation of complete blood counts, peripheral blood picture and detailed laboratory workup was the window to proper diagnosis and treatment in this case

Book of Abstracts of the 2nd International Conference on Applied Mathematics and Computational Sciences (ICAMCS-2022)

It is a great privilege for us to present the abstract book of ICAMCS-2022 to the authors and the delegates of the event. We hope that you will find it useful, valuable, aspiring, and inspiring. This book is a record of abstracts of the keynote talks, invited talks, and papers presented by the participants, which indicates the progress and state of development in research at the time of writing the research article. It is an invaluable asset to all researchers. The book provides a permanent record of this asset. Conference Title: 2nd International Conference on Applied Mathematics and Computational SciencesConference Acronym: ICAMCS-2022Conference Date: 12-14 October 2022Conference Organizers: DIT University, Dehradun, IndiaConference Mode: Online (Virtual