134 research outputs found
Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems
We propose a simple, powerful, and flexible machine learning framework for
(i) reducing the search space of computationally difficult enumeration variants
of subset problems and (ii) augmenting existing state-of-the-art solvers with
informative cues arising from the input distribution. We instantiate our
framework for the problem of listing all maximum cliques in a graph, a central
problem in network analysis, data mining, and computational biology. We
demonstrate the practicality of our approach on real-world networks with
millions of vertices and edges by not only retaining all optimal solutions, but
also aggressively pruning the input instance size resulting in several fold
speedups of state-of-the-art algorithms. Finally, we explore the limits of
scalability and robustness of our proposed framework, suggesting that
supervised learning is viable for tackling NP-hard problems in practice.Comment: AAAI 201
Computing Minimum Rainbow and Strong Rainbow Colorings of Block Graphs
A path in an edge-colored graph is rainbow if no two edges of it are
colored the same. The graph is rainbow-connected if there is a rainbow path
between every pair of vertices. If there is a rainbow shortest path between
every pair of vertices, the graph is strongly rainbow-connected. The
minimum number of colors needed to make rainbow-connected is known as the
rainbow connection number of , and is denoted by . Similarly,
the minimum number of colors needed to make strongly rainbow-connected is
known as the strong rainbow connection number of , and is denoted by
. We prove that for every , deciding whether
is NP-complete for split graphs, which form a subclass
of chordal graphs. Furthermore, there exists no polynomial-time algorithm for
approximating the strong rainbow connection number of an -vertex split graph
with a factor of for any unless P = NP. We
then turn our attention to block graphs, which also form a subclass of chordal
graphs. We determine the strong rainbow connection number of block graphs, and
show it can be computed in linear time. Finally, we provide a polynomial-time
characterization of bridgeless block graphs with rainbow connection number at
most 4.Comment: 13 pages, 3 figure
On the fine-grained complexity of rainbow coloring
The Rainbow k-Coloring problem asks whether the edges of a given graph can be
colored in colors so that every pair of vertices is connected by a rainbow
path, i.e., a path with all edges of different colors. Our main result states
that for any , there is no algorithm for Rainbow k-Coloring running in
time , unless ETH fails.
Motivated by this negative result we consider two parameterized variants of
the problem. In Subset Rainbow k-Coloring problem, introduced by Chakraborty et
al. [STACS 2009, J. Comb. Opt. 2009], we are additionally given a set of
pairs of vertices and we ask if there is a coloring in which all the pairs in
are connected by rainbow paths. We show that Subset Rainbow k-Coloring is
FPT when parameterized by . We also study Maximum Rainbow k-Coloring
problem, where we are additionally given an integer and we ask if there is
a coloring in which at least anti-edges are connected by rainbow paths. We
show that the problem is FPT when parameterized by and has a kernel of size
for every (thus proving that the problem is FPT), extending the
result of Ananth et al. [FSTTCS 2011]
Suggestions to Improve Lean Construction Planning
The Last Planner SystemÂź has been one of the most popular lean construction tools that offers a solution to tackle the problems of production management on construction sites. Since its inception almost 20 years ago, construction companies across the world have implemented Last Planner with reported success. However, even as Last Planner was originally designed to address some shortcomings of the CPM method, a particular shortcoming â namely task continuity was not addressed directly. Also, excepting PPC and Reasons for Non Completion charts, there are no explicit visual tools offered by the Last Planner system. On the other hand, Line of Balance based approaches intrinsically support the consideration of task continuity, and offer a basic visual management approach in schedule representation. With some exceptions, Line of Balance is seen as a special technique applicable only in linear or repetitive work based schedules. The authors suggest that i) there is a need for a robust theory of planning and scheduling and ii) there is a need for a more suitable approach that addresses critical aspects of planning and scheduling function for example by integrating Line of Balance and Last Planner to provide a more robust support for construction scheduling
Chasing the Rainbow Connection: Hardness, Algorithms, and Bounds
We study rainbow connectivity of graphs from the algorithmic and graph-theoretic points of view. The study is divided into three parts. First, we study the complexity of deciding whether a given edge-colored graph is rainbow-connected. That is, we seek to verify whether the graph has a path on which no color repeats between each pair of its vertices. We obtain a comprehensive map of the hardness landscape of the problem. While the problem is NP-complete in general, we identify several structural properties that render the problem tractable. At the same time, we strengthen the known NP-completeness results for the problem. We pinpoint various parameters for which the problem is ïŹxed-parameter tractable, including dichotomy results for popular width parameters, such as treewidth and pathwidth. The study extends to variants of the problem that consider vertex-colored graphs and/or rainbow shortest paths. We also consider upper and lower bounds for exact parameterized algorithms. In particular, we show that when parameterized by the number of colors k, the existence of a rainbow s-t path can be decided in Oâ (2k ) time and polynomial space. For the highly related problem of ïŹnding a path on which all the k colors appear, i.e., a colorful path, we explain the modest progress over the last twenty years. Namely, we prove that the existence of an algorithm for ïŹnding a colorful path in (2 â Δ)k nO(1) time for some Δ > 0 disproves the so-called Set Cover Conjecture.Second, we focus on the problem of ïŹnding a rainbow coloring. The minimum number of colors for which a graph G is rainbow-connected is known as its rainbow connection number, denoted by rc(G). Likewise, the minimum number of colors required to establish a rainbow shortest path between each pair of vertices in G is known as its strong rainbow connection number, denoted by src(G). We give new hardness results for computing rc(G) and src(G), including their vertex variants. The hardness results exclude polynomial-time algorithms for restricted graph classes and also fast exact exponential-time algorithms (under reasonable complexity assumptions). For positive results, we show that rainbow coloring is tractable for e.g., graphs of bounded treewidth. In addition, we give positive parameterized results for certain variants and relaxations of the problems in which the goal is to save k colors from a trivial upper bound, or to rainbow connect only a certain number of vertex pairs.Third, we take a more graph-theoretic view on rainbow coloring. We observe upper bounds on the rainbow connection numbers in terms of other well-known graph parameters. Furthermore, despite the interest, there have been few results on the strong rainbow connection number of a graph. We give improved bounds and determine exactly the rainbow and strong rainbow connection numbers for some subclasses of chordal graphs. Finally, we pose open problems and conjectures arising from our work
Afroamerikkalaisen urheilijan kapina : âOlympic Project for Human Rightsâ ja afroamerikkalaisten nĂ€kemykset Philadelphia Tribunen ja Los Angeles Sentinelin kirjoituksissa syyskuusta 1967 elokuuhun 1968
Tutkielma kĂ€sittelee kuinka Los Angeles Sentinel ja Philadelphia Tribune kuvailevat afroamerikkalaisten keskuudessa syntyneitĂ€ nĂ€kemyksiĂ€ OPHR:ÀÀn liittyen syyskuusta 1967 elokuuhun 1968. OPHR eli âOlympic Project for Human Rightsâ oli kansalaisoikeusaktivisti ja sosiologi Harry Edwardsin lokakuussa 1967 perustama organisaatio, joka vastusti rasismia ja pyrki jĂ€rjestĂ€mÀÀn afroamerikkalaisten urheilijoiden olympiaboikotin. Boikotti ei lopulta toteutunut, mutta organisaatio pyrkimyksineen sai paljon huomiota. Sentinel ja Tribune ovat molemmat afroamerikkalaisia sanomalehtiĂ€, joiden kirjoittajat olivat myös afroamerikkalaisia. Tutkielmassa tarkastellaan siis ilmiötĂ€ afroamerikkalaisesta nĂ€kökulmasta.
LÀhilukua hyödyntÀmÀllÀ ja vertailemalla molempien sanomalehtien toimittajien ja kolumnistien nÀkemyksiÀ tuli esille, ettÀ OPHR ja olympiaboikotin uhka herÀttivÀt vastakkaisia nÀkemyksiÀ afroamerikkalaisten keskuudessa kolmen eri teeman kohdalla. NÀistÀ ensimmÀinen liittyi urheilun rooliin. Tuohon aikaan eli vielÀ voimakkaana mielikuva urheilusta suurena tasa-arvoistajana ja moni afroamerikkalainenkin uskoi urheilun edistÀneen heidÀn asemaansa. TÀtÀ kÀytettiin SentinelissÀ ja Tribunessa argumenttina olympiaboikottia vastaan. Toisaalta olympiaboikotin kannattajat huomauttivat, ettÀ urheilussa afroamerikkalaiset kohtasivat yhtÀ lailla rotusyrjintÀÀ.
Toiseksi afroamerikkalaisten keskuudessa oltiin eri mieltÀ parhaista keinoista heidÀn asioidensa ajamiseksi. Osa toimittajista ja kolumnisteista kritisoi OPRH:n toimintaa kuten vÀkivallalla uhkaamista ja piti olympiaboikottia hyödyttömÀnÀ. Toiset taas kehuivat OPHR:ÀÀ ja erityisesti nuorten urheilijoiden aktivismia. Vastakkainasettelua taustoittaa se, ettÀ osa afroamerikkalaisista ei katsonut kansalaisoikeusliikkeen rauhanomaisen protestoinnin riittÀvÀn vaan vaati radikaalimpaa toimintaa. Mustan vallan liike vaikutti merkittÀvÀsti Edwardsin ajattelun ja OPHR:n toiminnan taustalla.
LisÀksi SentinelissÀ ja Tribunessa kirjoitettiin Edwardsista eri tavoin. Edwards sai kiitosta afroamerikkalaisten kohtaaman syrjinnÀn esille nostamisesta. Edwards oli kuitenkin myös provosoiva puheissaan ja olemukseltaan ja hÀn kohtasi myös paljon kritiikkiÀ
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