Planar Induced Subgraphs of Sparse Graphs

We show that every graph has an induced pseudoforest of at least $n-m/4.5$ vertices, an induced partial 2-tree of at least $n-m/5$ vertices, and an induced planar subgraph of at least $n-m/5.2174$ vertices. These results are constructive, implying linear-time algorithms to find the respective induced subgraphs. We also show that the size of the largest $K_h$-minor-free graph in a given graph can sometimes be at most $n-m/6+o(m)$.Comment: Accepted by Graph Drawing 2014. To appear in Journal of Graph Algorithms and Application

Parameterized Study of the Test Cover Problem

We carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the {\sc Test Cover} problem we are given a set $[n]=\{1,...,n\}$ of items together with a collection, $\cal T$, of distinct subsets of these items called tests. We assume that $\cal T$ is a test cover, i.e., for each pair of items there is a test in $\cal T$ containing exactly one of these items. The objective is to find a minimum size subcollection of $\cal T$, which is still a test cover. The generic parameterized version of {\sc Test Cover} is denoted by $p(k,n,|{\cal T}|)$-{\sc Test Cover}. Here, we are given $([n],\cal{T})$ and a positive integer parameter $k$ as input and the objective is to decide whether there is a test cover of size at most $p(k,n,|{\cal T}|)$. We study four parameterizations for {\sc Test Cover} and obtain the following: (a) $k$-{\sc Test Cover}, and $(n-k)$-{\sc Test Cover} are fixed-parameter tractable (FPT). (b) $(|{\cal T}|-k)$-{\sc Test Cover} and $(\log n+k)$-{\sc Test Cover} are W[1]-hard. Thus, it is unlikely that these problems are FPT

The Parameterized Complexity of Domination-type Problems and Application to Linear Codes

We study the parameterized complexity of domination-type problems. (sigma,rho)-domination is a general and unifying framework introduced by Telle: a set D of vertices of a graph G is (sigma,rho)-dominating if for any v in D, |N(v)\cap D| in sigma and for any $v\notin D, |N(v)\cap D| in rho. We mainly show that for any sigma and rho the problem of (sigma,rho)-domination is W[2] when parameterized by the size of the dominating set. This general statement is optimal in the sense that several particular instances of (sigma,rho)-domination are W[2]-complete (e.g. Dominating Set). We also prove that (sigma,rho)-domination is W[2] for the dual parameterization, i.e. when parameterized by the size of the dominated set. We extend this result to a class of domination-type problems which do not fall into the (sigma,rho)-domination framework, including Connected Dominating Set. We also consider problems of coding theory which are related to domination-type problems with parity constraints. In particular, we prove that the problem of the minimal distance of a linear code over Fq is W[2] for both standard and dual parameterizations, and W[1]-hard for the dual parameterization. To prove W[2]-membership of the domination-type problems we extend the Turing-way to parameterized complexity by introducing a new kind of non deterministic Turing machine with the ability to perform `blind' transitions, i.e. transitions which do not depend on the content of the tapes. We prove that the corresponding problem Short Blind Multi-Tape Non-Deterministic Turing Machine is W[2]-complete. We believe that this new machine can be used to prove W[2]-membership of other problems, not necessarily related to dominationComment: 19 pages, 2 figure

Íslensk börn og unglingar með höfuðáverka : hve margir þurfa sérhæfða fræðslu, endurhæfingu eða eftirfylgd og hvers konar íhlutun er við hæfi?

Neðst á síðunni er hægt að nálgast greinina í heild sinni með því að smella á hlekkinn View/OpenTilgangur rannsóknarinnar var að kanna fjölda barna og unglinga, sem lýsa eftirstöðvum fjórum árum eftir höfuðáverka, og skoða eðli þessara kvartana, og meta þannig þörf fyrir sérhæfða íhlutun af mismunandi toga. Gögnum var safnað á framvirkan hátt um alla sjúklinga 0-19 ára, sem greindir voru með höfuðáverka (ICD-9 850-854) á Borgarspítalanum á einu ári, 1992-1993 (n=405). Fjórum árum síðar var spurningalisti um eftirstöðvar áverka sendur til sjúklinga. Alvarleikastig byggt á eðli kvartana var metið samkvæmt viðmiðum Glasgow Outcome Scale (GOS), barnaútgáfu. Alls lýstu 39 sjúklingar lýstu eftirstöðvum höfuðáverka fjórum árum síðar. Samkvæmt viðmiðum GOS lýstu 19 þeirra góðri útkomu (e. good outcome), 14 lýstu miðlungs hömlun (e. moderate disability), 2 lýstu alvarlegri hömlun (severe disability) og 4 höfðu látist vegna heilaskaða. Nýleg athugun bendir til þess að ekki hafi orðið fækkun á börnum og unglingum sem hljóta alvarlegri höfuðáverka (ICD-9 851- 854) á ári hverju.Niðurstöður benda til þess að tugir íslenskra barna og unglinga þarfnist sérhæfðrar íhlutunar og eftirfylgdar á ári hverju vegna afleiðinga höfuðáverka. Íhlutunin getur verið mjög breytileg, allt frá fræðslu fyrir foreldra til endurhæfingar og eftirfylgdar til lengri tíma. Íhlutunin þarf að taka mið af vanda hvers og eins

Extremely Low Birthweight Infants in Iceland. Health and development

Neðst á síðunni er hægt að nálgast greinina í heild sinni með því að smella á hlekkinn View/OpenObjective: Survival of extremely low birthweight infants (BW<1000g) in Iceland has increased in recent years, especially since the availability of surfactant therapy for Respiratory Distress Syndrome of Prematurity. This study was part of a geographically defined national study on survival, health, development and longterm outcome of extremely low birthweight (ELBW) infants in Iceland focusing on health, development and disabilities with reference to a control group. Material and methods: Information from the National Birth Registry on births in Iceland of ELBW infants weighing 500-999g was collected in two periods 1982-90 and 1991-95, before and after surfactant therapy became available. Information on pregnancy, birth, diseases in the newborn period and later health problems was collected from hospital records. The ELBW infants born in 1991-95 and matched control children were enrolled to a prospective study on longterm health and development. The children undervent medical examinations and developmental testing at 5 years of age in 1996-2001. Comparison was made between the two groups of ELBW infants and between ELBW infants and control children born in 1991-95. Results: In 1982-90 the longterm survival of ELBW infants at 5 years of age was 22% and 52% in 1991-95. In both periods 1982-90 and 1991-95 similar data was found on ELBW infants regarding mothers health, pregnancy, birth and neonatal period. Difference was found in maternal age being significantly higher (p=0.02) and significally more deliveries by cesarian section (p=0.02) in the latter period. The two groups of ELBW infants were similar regarding sex, birthweight and diseases in the newborn period. Comparison between 35 ELBW infants and 55 control children born 1991-95 showed that significantly more mothers of ELBW children smoked during pregnancy (p=0.003) and suffered from various diseases (p=0.001). More ELBW children were born by cesarian section (p=0.001) than control children and their parents reported more longterm health problems regarding astma (p=0.001), convulsions (p=0.001), difficulties in swallowing (p=0.001) and weight gaining (p=0.005). At five years of age significantly more ELBW children born in 1991-95 compared to control children had abnormal general physical examination (p=<0.001), neurological examination (p=<0.001) and motor skills (p=<0.001). Scores on developmental testing were significantly lower (p=0.002). The proportion of ELBW children with disabilities was 16% in 1982-90 and 14% in 1991-95. Conclusions: The two groups of ELBW infants born in 1982-90 and 1991-95 are similar regarding problems during pregnancy, birth and newborn period. The proportion of children with disabilities is similar in both periods although survival was significantly increased. When compared to matched control children, ELBW children born in 1991-95 suffer significantly more longterm health and developmental problems.Inngangur: Lífslíkur lítilla fyrirbura með fæðingarþyngd <1000 g hafa aukist verulega hin síðari ár einkum eftir að notkun lungnablöðruseytis (surfactants) við glærhimnusjúkdómi (Hyalin Membrane Disease/ HMD) varð almenn. Hluti þessara barna glímir við langvinn og alvarleg heilsuvandamál. Tilgangur rannsóknarinnar ,,Fyrirburar - langtímaeftirlit með heilsu og þroska" var að varpa ljósi á lífslíkur, heilsufar, þroska og langtímahorfur lítilla fyrirbura á Íslandi í samanburði við fullburða jafnaldra og fjallar þessi hluti hennar um heilsufar, þroska og fötlun. Efniviður og aðferðir: Aflað var upplýsinga úr tölvuskrá Fæðingarskráningar Ríkisspítala um fæðingar lítilla fyrirbura sem vógu 500-999 g og fæddust á tveimur tímabilum, 1982-90 og 1991-95, fyrir og eftir að notkun lungnablöðruseytis varð almenn. Leitað var að upplýsingum varðandi meðgöngu, fæðingu, sjúkdóma á nýburatíma og síðari heilsufarsvandamál í sjúkraskrám. Fyrirburar áranna 1991-95 og jafnaldra samanburðarbörn tóku þátt í framskyggnri rannsókn á heilsu og þroska. Börnin komu til skoðunar við rúmlega fimm ára aldur á árunum 1996-2001 og gengust undir þroskamælingar. Við úrvinnslu var annars vegar gerður samanburður á fyrirburahópunum tveimur og hins vegar samanburður á fyrirburum og samanburðarbörnum áranna 1991-95. Niðurstöður: Á árunum 1982-90 lifðu 22% af lifandi fæddum litlum fyrirburum við 5 ára aldur og 52% á seinna tímabilinu 1991-95. Á báðum tímabilum fengust svipaðar upplýsingar um fyrirburamæður, meðgöngu og fæðingu lítilla fyrirbura. Marktækur munur var hvað varðar hærri aldur mæðra (p=0,02) og fjölda fæðinga með keisaraskurði á seinna tímabilinu (p=0,02). Ekki var marktækur munur milli fyrirburahópanna hvað varðar kyn, fæðingarþyngd eða sjúkdóma á nýburatíma. Samanburður milli 35 fyrirbura og 55 samanburðarbarna áranna 1991-95 leiddi í ljós að fleiri mæður fyrirbura reyktu (p=0,003) og glímdu við sjúkdóma á meðgöngu (p=<0,001) og að fleiri fyrirburar fæddust með keisarskurði (p=0,001). Marktækur munur var á heilsufari fyrirbura og samanburðarbarna hvað varðar asma (p=<0,001), krampa (p=<0,001), kyngingarerfiðleika (p=0,001) og erfiðleika með að þyngjast (p=0,005). Athugun við fimm ára aldur leiddi í ljós að miðað við samanburðarbörn voru marktækt fleiri fyrirburar áranna 1991-95 með frávik við almenna skoðun (p=<0,001), taugalæknisfræðilega skoðun (p=<0,001) og við mat á hreyfifærni (p=<0,001). Niðurstöður þroskamælinga voru marktækt lægri (p=0,002). Svipað hlutfall fyrirbura var með fötlun á báðum tímabilum, 16% árin 1982-90 og 14% árin 1991-95. Ályktun: Fyrirburahópar áranna 1982-90 og 1991-95 voru svipaðir hvað varðar heilsufar á meðgöngu, fæðingu og sjúkdóma eftir fæðingu. Hlutfall barna með fötlun var svipað á báðum tímabilum þrátt fyrir marktækt aukna lifun. Samanburður lítilla fyrirbura áranna 1991-95 við jafnaldra samanburðarbörn sýndi að litlir fyrirburar voru með marktækt meiri heilsufarsvandamál og þroskafrávik

An Efficient Local Search for Partial Latin Square Extension Problem

A partial Latin square (PLS) is a partial assignment of n symbols to an nxn grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. In this paper we propose an efficient local search for this problem. We focus on the local search such that the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and then assigning symbols to at most q empty cells. For p in {1,2,3}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n^{p+1}) time. We also propose a novel swap operation, Trellis-swap, which is a generalization of (1,q)-swap and (2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to do the same thing. Using these neighborhood search algorithms, we design a prototype iterated local search algorithm and show its effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.Comment: 17 pages, 2 figure

GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer), provides a unified framework for scalable computation and presentation of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems. Efficient representation and applicability to large-scale graphs and complex networks are particularly considered in its design. The problems currently supported include maximum clique, graph colouring, maximum independent set, minimum vertex clique covering, minimum dominating set, as well as the longest simple cycle problem. Suboptimal solutions and intervals for optimal objective values are estimated using scalable heuristics. The tool is designed with extensibility in mind, with the view of further problems and both new fast and high-performance heuristics to be added in the future. GraphCombEx has already been successfully used as a support tool in a number of recent research studies using combinatorial optimisation to analyse complex networks, indicating its promise as a research software tool

Approximating the double-cut-and-join distance between unsigned genomes

In this paper we study the problem of sorting unsigned genomes by double-cut-and-join operations, where genomes allow a mix of linear and circular chromosomes to be present. First, we formulate an equivalent optimization problem, called maximum cycle/path decomposition, which is aimed at finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths in a breakpoint graph. Then, we show that the problem of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length no more than l can be reduced to the well-known degree-bounded k-set packing problem with k = 2l. Finally, a polynomial-time approximation algorithm for the problem of sorting unsigned genomes by double-cut-and-join operations is devised, which achieves the approximation ratio for any positive ε. For the restricted variation where each genome contains only one linear chromosome, the approximation ratio can be further improved t