Polynomial kernels for 3-leaf power graph modification problems

A graph G=(V,E) is a 3-leaf power iff there exists a tree T whose leaves are V and such that (u,v) is an edge iff u and v are at distance at most 3 in T. The 3-leaf power graph edge modification problems, i.e. edition (also known as the closest 3-leaf power), completion and edge-deletion, are FTP when parameterized by the size of the edge set modification. However polynomial kernel was known for none of these three problems. For each of them, we provide cubic kernels that can be computed in linear time for each of these problems. We thereby answer an open problem first mentioned by Dom, Guo, Huffner and Niedermeier (2005).Comment: Submitte

An Insider’s Framework of Inclusive Excellence

Over the past few years, there has been an increase in libraries recruiting positions such as DEI Librarian, Librarian for Inclusion, and Director of Diversity, Equity, Inclusion and Organizational Excellence. The positions are often vague about the job responsibilities but specific about the expectations of promoting EDI- whether in collections, staff, or culture. This article explores this DEI work through an interview with Ione Damasco, the Associate Dean for Inclusive Excellence, Engagement, and Operations at the University of Dayton

Collections Amplifying Diverse Voices

This article explores the creation, implementation, and maintenance of American University Library\u27s Collections Amplifying Diverse Voices

Minimal Conflicting Sets for the Consecutive Ones Property in ancestral genome reconstruction

A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1's on each row are consecutive. A Minimal Conflicting Set is a set of rows that does not have the C1P, but every proper subset has the C1P. Such submatrices have been considered in comparative genomics applications, but very little is known about their combinatorial structure and efficient algorithms to compute them. We first describe an algorithm that detects rows that belong to Minimal Conflicting Sets. This algorithm has a polynomial time complexity when the number of 1's in each row of the considered matrix is bounded by a constant. Next, we show that the problem of computing all Minimal Conflicting Sets can be reduced to the joint generation of all minimal true clauses and maximal false clauses for some monotone boolean function. We use these methods on simulated data related to ancestral genome reconstruction to show that computing Minimal Conflicting Set is useful in discriminating between true positive and false positive ancestral syntenies. We also study a dataset of yeast genomes and address the reliability of an ancestral genome proposal of the Saccahromycetaceae yeasts.Comment: 20 pages, 3 figure

A structural approach to kernels for ILPs: Treewidth and Total Unimodularity

Kernelization is a theoretical formalization of efficient preprocessing for NP-hard problems. Empirically, preprocessing is highly successful in practice, for example in state-of-the-art ILP-solvers like CPLEX. Motivated by this, previous work studied the existence of kernelizations for ILP related problems, e.g., for testing feasibility of Ax <= b. In contrast to the observed success of CPLEX, however, the results were largely negative. Intuitively, practical instances have far more useful structure than the worst-case instances used to prove these lower bounds. In the present paper, we study the effect that subsystems with (Gaifman graph of) bounded treewidth or totally unimodularity have on the kernelizability of the ILP feasibility problem. We show that, on the positive side, if these subsystems have a small number of variables on which they interact with the remaining instance, then we can efficiently replace them by smaller subsystems of size polynomial in the domain without changing feasibility. Thus, if large parts of an instance consist of such subsystems, then this yields a substantial size reduction. We complement this by proving that relaxations to the considered structures, e.g., larger boundaries of the subsystems, allow worst-case lower bounds against kernelization. Thus, these relaxed structures can be used to build instance families that cannot be efficiently reduced, by any approach.Comment: Extended abstract in the Proceedings of the 23rd European Symposium on Algorithms (ESA 2015

Parameterized Algorithms for Modular-Width

It is known that a number of natural graph problems which are FPT parameterized by treewidth become W-hard when parameterized by clique-width. It is therefore desirable to find a different structural graph parameter which is as general as possible, covers dense graphs but does not incur such a heavy algorithmic penalty. The main contribution of this paper is to consider a parameter called modular-width, defined using the well-known notion of modular decompositions. Using a combination of ILPs and dynamic programming we manage to design FPT algorithms for Coloring and Partitioning into paths (and hence Hamiltonian path and Hamiltonian cycle), which are W-hard for both clique-width and its recently introduced restriction, shrub-depth. We thus argue that modular-width occupies a sweet spot as a graph parameter, generalizing several simpler notions on dense graphs but still evading the "price of generality" paid by clique-width.Comment: to appear in IPEC 2013. arXiv admin note: text overlap with arXiv:1304.5479 by other author

Komunikasi Digital Melalui Seni Arca

Penyelidikkan ini bertujuan mengkaji siri karya seni arca dengan cara menganalisa komunikasi digital melalui teknologi mobil. Teknologi mobil merupakan satu kaedah komunikasi popular di abad ke 21. Pengarca mengaplikasikan komunikasi digital melalui pelantar teknologi mobil sebagai medium dalam penghasilan karya. Penyelidikan ini menggunakan kaedah praktis studio melalui kajian yang melibatkan eksperimentasi. Justeru itu, fabrikasi bentuk menerusi modifikasi dan manipulasi menjadi teras dalam proses eksperimentasi kajian seni arca. Di Malaysia, pendekatan komunikasi digital sebagai medium adalah sangat terhad. Ini disebabkan oleh perkembangan seni arca di Malaysia adalah terkebelakang berbanding barat. Objektif penyelidikan ini adalah untuk mengembangkan komunikasi digital merentasi media dalam konteks seni arca dan merupakan medium baru dalam bidang seni kontemporari. Teknologi mobil merupakan keperluan bagi generasi hari ini kerana kepentingan multi fungsinya. Peranti mudah alih, pada suatu ketika dahulu dianggap sebagai barang mewah yang hanya digunakan oleh individu tertentu sahaja. Namun, kini telah menjadi gaya hidup digital dan mampu dimiliki oleh setiap golongan masyarakat tanpa mengira usia atau pun jantina. Disebalik perkembangan teknologi mudah alih ini, fungsi gajet telah menjadi begitu penting melibatkan beberapa bidang utama di dalam kehidupan. Ia mempengaruhi serta membentuk budaya komunikasi dan hiburan. Hasil kajian ini mendapati komunikasi digital dalam kontek seni arca menjelaskan kebergantugan dan interaksi manusia dengan mesin melalui gaya hidup digital. Ia merupakan suatu ekspresi terhadap aspirasi, emosi dan obsesi yang menjelaskan gaya hidup digital masa kin

On Structural Parameterizations of Hitting Set: Hitting Paths in Graphs Using 2-SAT

Hitting Set is a classic problem in combinatorial optimization. Its input consists of a set system F over a finite universe U and an integer t; the question is whether there is a set of t elements that intersects every set in F. The Hitting Set problem parameterized by the size of the solution is a well-known W[2]-complete problem in parameterized complexity theory. In this paper we investigate the complexity of Hitting Set under various structural parameterizations of the input. Our starting point is the folklore result that Hitting Set is polynomial-time solvable if there is a tree T on vertex set U such that the sets in F induce connected subtrees of T. We consider the case that there is a treelike graph with vertex set U such that the sets in F induce connected subgraphs; the parameter of the problem is a measure of how treelike the graph is. Our main positive result is an algorithm that, given a graph G with cyclomatic number k, a collection P of simple paths in G, and an integer t, determines in time 2^{5k} (|G| +|P|)^O(1) whether there is a vertex set of size t that hits all paths in P. It is based on a connection to the 2-SAT problem in multiple valued logic. For other parameterizations we derive W[1]-hardness and para-NP-completeness results.Comment: Presented at the 41st International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2015. (The statement of Lemma 4 was corrected in this update.