Stable Matching Games: Manipulation via Subgraph Isomorphism

In this paper we consider a problem that arises from a strategic issue in the stable matching model (with complete preference lists) from the viewpoint of exact-exponential time algorithms. Specifically, we study the Stable Extension of Partial Matching (SEOPM) problem, where the input consists of the complete preference lists of men, and a partial matching. The objective is to find (if one exists) a set of preference lists of women, such that the men-optimal Gale Shapley algorithm outputs a perfect matching that contains the given partial matching. Kobayashi and Matsui [Algorithmica, 2010] proved this problem is NP-complete. In this article, we give an exact-exponential algorithm for SEOPM running in time 2^{O(n)}, where n denotes the number of men/women. We complement our algorithmic finding by showing that unless Exponential Time Hypothesis (ETH) fails, our algorithm is asymptotically optimal. That is, unless ETH fails, there is no algorithm for SEOPM running in time 2^{o(n)}. Our algorithm is a non-trivial combination of a parameterized algorithm for Subgraph Isomorphism, a relationship between stable matching and finding an out-branching in an appropriate graph and enumerating non-isomorphic out-branchings

Knot Ready: Lessons From India on Delaying Marriage for Girls

Examines trends in and predictors of age at marriage. Assesses the effectiveness of ten program and policy interventions, underlying factors, and lessons for expanding viable strategies: empower girls, mobilize communities, and influence decision makers

How to assign volunteers to tasks compatibly ? A graph theoretic and parameterized approach

In this paper we study a resource allocation problem that encodes correlation between items in terms of \conflict and maximizes the minimum utility of the agents under a conflict free allocation. Admittedly, the problem is computationally hard even under stringent restrictions because it encodes a variant of the {\sc Maximum Weight Independent Set} problem which is one of the canonical hard problems in both classical and parameterized complexity. Recently, this subject was explored by Chiarelli et al.~[Algorithmica'22] from the classical complexity perspective to draw the boundary between {\sf NP}-hardness and tractability for a constant number of agents. The problem was shown to be hard even for small constant number of agents and various other restrictions on the underlying graph. Notwithstanding this computational barrier, we notice that there are several parameters that are worth studying: number of agents, number of items, combinatorial structure that defines the conflict among the items, all of which could well be small under specific circumstancs. Our search rules out several parameters (even when taken together) and takes us towards a characterization of families of input instances that are amenable to polynomial time algorithms when the parameters are constant. In addition to this we give a superior 2^{m}|I|^{\Co{O}(1)} algorithm for our problem where $m$ denotes the number of items that significantly beats the exhaustive \Oh(m^{m}) algorithm by cleverly using ideas from FFT based fast polynomial multiplication; and we identify simple graph classes relevant to our problem's motivation that admit efficient algorithms

Relative Interval Analysis of Paging Algorithms on Access Graphs

Access graphs, which have been used previously in connection with competitive analysis and relative worst order analysis to model locality of reference in paging, are considered in connection with relative interval analysis. The algorithms LRU, FIFO, FWF, and FAR are compared using the path, star, and cycle access graphs. In this model, some of the expected results are obtained. However, although LRU is found to be strictly better than FIFO on paths, it has worse performance on stars, cycles, and complete graphs, in this model. We solve an open question from [Dorrigiv, Lopez-Ortiz, Munro, 2009], obtaining tight bounds on the relationship between LRU and FIFO with relative interval analysis.Comment: IMADA-preprint-c

Resolute control: Forbidding candidates from winning an election is hard

publishedVersio

Bioinformatics tools for development of fast and cost effective simple sequence repeat (SSR), and single nucleotide polymorphisms (SNP) markers from expressed sequence tags (ESTs)

The development of current molecular biology techniques has led to the generation of huge amount of gene sequence information under the expressed sequence tag (EST) sequencing projects on a large number of plant species. This has opened a new era in crop molecular breeding with identification and/or development of a new class of useful DNA markers called genic molecular markers (GMMs). These markers represent the functional component of the genome in contrast to all other random DNA markers (RMMs). Many recent studies have demonstrated that GMMs may be superior to RMMs for use in the marker assisted selection, comparative mapping and exploration of functional genetic diversity in the germplasms adapted to different environment. Therefore, identification of DNA sequences which can be used as markers remains fundamental to the development of GMMs. Amongst others; bioinformatics approaches are very useful for development of molecular markers, making their development much faster and cheaper. Already, a number of computer programs have been implemented that aim at identifying molecular markers from sequence data. A revision of current bioinformatics tools for development of genic molecular markers is, therefore, crucial in this phase. This mini-review mainly provides an overview of different bioinformatics tools available and its use in marker development with particular reference to SNP and SSR markers.Keywords: Genic molecular marker, simple sequence repeat (SSR), and single nucleotide polymorphisms (SNP) markers from expressed sequence tags (ESTs).African Journal of Biotechnology Vol. 12(30), pp. 4713-472