32 research outputs found
Lower Bounds for the Graph Homomorphism Problem
The graph homomorphism problem (HOM) asks whether the vertices of a given
-vertex graph can be mapped to the vertices of a given -vertex graph
such that each edge of is mapped to an edge of . The problem
generalizes the graph coloring problem and at the same time can be viewed as a
special case of the -CSP problem. In this paper, we prove several lower
bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main
result is a lower bound .
This rules out the existence of a single-exponential algorithm and shows that
the trivial upper bound is almost asymptotically
tight.
We also investigate what properties of graphs and make it difficult
to solve HOM. An easy observation is that an upper
bound can be improved to where
is the minimum size of a vertex cover of . The second
lower bound shows that the upper bound is
asymptotically tight. As to the properties of the "right-hand side" graph ,
it is known that HOM can be solved in time and
where is the maximum degree of
and is the treewidth of . This gives
single-exponential algorithms for graphs of bounded maximum degree or bounded
treewidth. Since the chromatic number does not exceed
and , it is natural to ask whether similar
upper bounds with respect to can be obtained. We provide a negative
answer to this question by establishing a lower bound for any
function . We also observe that similar lower bounds can be obtained for
locally injective homomorphisms.Comment: 19 page
Algebraic Theory of Promise Constraint Satisfaction Problems, First Steps
What makes a computational problem easy (e.g., in P, that is, solvable in
polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a
satisfactory answer for a quite broad class of computational problems, so
called fixed-template constraint satisfaction problems (CSPs) -- it has turned
out that their complexity is captured by a certain specific form of symmetry.
This paper explains an extension of this theory to a much broader class of
computational problems, the promise CSPs, which includes relaxed versions of
CSPs such as the problem of finding a 137-coloring of a 3-colorable graph
Complete tree subset difference broadcast encryption scheme and its analysis
The subset difference (SD) method proposed by Naor, Naor and Lotspiech is the most popular broadcast encryption (BE) scheme. It is suitable for real-time applications like Pay-TV and has been suggested for use by the AACS standard for digital rights management in Blu-Ray and HD-DVD discs. The SD method assumes the number of users to be a power of two. We propose the complete tree subset difference (CTSD) method that allows the system to support an arbitrary number of users. In particular, it subsumes the SD method and all results proved for the CTSD method also hold for the SD method. Recurrences are obtained for the CTSD scheme to count the number, N(n, r, h), of possible ways r users in the system of n users can be revoked to result in a transmission overhead or header length of h. The recurrences lead to a polynomial time dynamic programming algorithm for computing N(n, r, h). Further, they provide bounds on the maximum possible header length. A probabilistic analysis is performed to obtain an O(r log n) time algorithm to compute the expected header length in the CTSD scheme. Further, for the SD scheme we obtain an explicit limiting upper bound on the expected header length
Oksidacijski stres u lakirera izloženih niskim razinama olova
Lead toxicity is a public health problem particularly to the children and to occupationally exposed adults. Evidence is mounting successively regarding the adverse health effects of lead at low levels. This study was undertaken to assess the antioxidant status of lead-exposed residential and commercial painters of Lucknow city in Uttar Pradesh, India. Thirty-five painters aged 20 to 50 years who had blood lead levels ≤400 µg L-1 were selected for the study from a population of 56 male painters initially screened for blood lead. The control group included an equal number of subjects of the same age group without any occupational exposure to lead. We studied the association between low lead level exposure and antioxidant status and found that blood lead levels in painters were approximately seven times as high as in controls [(219.2 ± 61.9) µg L-1 vs. (30.6±10.1) µg L-1, respectively]. Among the biomarkers of lead toxicity a significant decrease in the level of delta-aminolevulinic acid dehydratase [(9.13±4.62) UL-1 vs. (39.38±5.05) UL-1] and an increase in the level of zinc protoporphyrin [(187.9±49.8) µg L-1 vs. (26.4±5.5) µg L-1] were observed in painters compared to controls. Among antioxidant enzymes, painters showed a significant decrease in catalase [(56.77±11.11) UL-1 vs. (230.30±42.55) UL-1] and superoxide dismutase [(0.64±0.19) UL-1 vs. (2.68±0.62) UL-1] compared to controls. Lipid peroxidation was monitored by measuring thiobarbituric acid reactive substances (TBARS) that were expressed in terms of malondialdehyde (MDA) equivalents. Concentration of MDA in plasma was higher in painters than in controls [(7.48±1.31) nmol mL-1 vs. (3.08±0.56) nmol mL-1]. Significant changes were also observed in reduced and oxidised glutathione levels. The strong association between blood lead levels and oxidative stress markers in this population suggests that oxidative stress should be considered in the pathogenesis of lead-related diseases among people with low level environmental exposure to lead.Toksičnost olova javnozdravstveni je problem, napose u djece i odraslih osoba koje su im izložene profesionalno. Sve je više dokaza o štetnom djelovanju olova pri niskim razinama. Svrha je ovog ispitivanja bila procijeniti antioksidacijski status u lakirera iz grada Lucknowa u indijskoj pokrajini Uttar Pradesh. Iz skupine od 56 muškaraca lakirera u dobi od 20 do 50 godina s pozitivnim početnim nalazima olova u krvi, za ispitivanje su izabrana 35-orica čije su razine iznosile ≤400 µg L-1. Izabran je i jednaki broj kontrolnih ispitanika iz iste dobne skupine, koji nisu bili profesionalno izloženi olovu. Ispitana je povezanost izme|u izloženosti niskim razinama olova i antioksidacijskoga stanja te je utvrđeno da su razine olova u krvi lakirera [(219,2±61,9) µg L-1] bile oko sedam puta više negoli u kontrolnih ispitanika [(30,6±10,1) µg L-1]. Od biopokazatelja toksičnosti olova u lakirera je zamijećen značajan pad razina delta- ALAD [(9,13±4,62) UL-1 prema (39,38±5,05) UL-1] te rast razina cinkova protoporfirina [(187,9±49,8) µg L-1 prema (26,4±5,5) µg L-1] u odnosu na kontrolne ispitanike. Od antioksidacijskih enzima u lakirera je značajno pala aktivnost katalaze [(56,77±11,11) UL-1 prema (230,30±42,55) UL-1] i superoksid dismutaze [(0,64±0.19) UL-1 prema (2,68±0,62) UL-1] u odnosu na kontrolu, dok je produkt lipidne peroksidacije u plazmi (izv. thiobarbituric acid reactive substances, TBARS) izražen kao koncentracija malondialdehida (MDA) porastao [(7,48±1,31) nmol mL-1 prema (3,08±0,56) nmol mL-1]. Značajne su promjene također zamijećene u smanjenim razinama glutationa i njihovoj oksidaciji. Snažna povezanost razina olova u krvi s pokazateljima oksidacijskoga stresa upućuje na to da u osoba s niskom razinom izloženosti olovu iz okoliša kod razmatranja patogeneze bolesti povezane s olovom u obzir valja uzeti oksidacijski stres