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Problem in combinatorial optimization
combinatorial optimization, submodular flow is a general class of optimization problems that includes as special cases the minimum-cost flow problem, matroid intersection
Submodular_flow
Method to solve optimization problems
well-known integral LPs include the matching polytope, lattice polyhedra, submodular flow polyhedra, and the intersection of two generalized polymatroids/g-polymatroids
Linear_programming
Edges that hit all cycles in a graph
Gabow, Harold N. (1993), "A framework for cost-scaling algorithms for submodular flow problems", 34th Annual Symposium on Foundations of Computer Science
Feedback_arc_set
American/Canadian mathematician and computer scientist
graphs from the point of view of matchings. He introduced polymatroids, submodular flows with Richard Giles, and the terms clutter and blocker in the study
Jack_Edmonds
Edges crossing all dicuts in a directed graph
graph can be found in polynomial time, and is a special case of the submodular flow problem. In planar graphs, dijoins and feedback arc sets are dual concepts
Dijoin
Graph representing faces of another graph
MR 1857074. Gabow, Harold N. (1995), "Centroids, representations, and submodular flows", Journal of Algorithms, 18 (3): 586–628, doi:10.1006/jagm.1995.1022
Dual_graph
Sequence of locally optimal choices
solution at least half the value of the optimal solution. Solutions for submodular maximization are approximated using a greedy algorithm which yields a
Greedy_algorithm
Computer-based method for summarizing a text
submodular optimization. For example, the set cover problem is a special case of submodular optimization, since the set cover function is submodular.
Automatic_summarization
Combinatorial optimization method for a family of functions of discrete variables
function with a similar but submodular one, for instance truncating all non-submodular terms or replacing them with similar submodular expressions. Such approach
Graph_cut_optimization
MR 0258678 Gabow, Harold N. (1995), "Centroids, representations, and submodular flows", Journal of Algorithms, 18 (3): 586–628, doi:10.1006/jagm.1995.1022
Lucchesi–Younger_theorem
valuation is a submodular set function. The converse is not necessarily true. This is shown by the example on the right. The utility is submodular since it
Gross substitutes (indivisible items)
Gross_substitutes_(indivisible_items)
Combinatorial optimization method for pseudo-Boolean functions
f} is submodular then QPBO produces a global optimum equivalently to graph cut optimization, while if f {\displaystyle f} contains non-submodular terms
Quadratic pseudo-Boolean optimization
Quadratic_pseudo-Boolean_optimization
Economical computational problem
game is called submodular if (a) the set of feasible joint decisions is a sublattice; (b) the cost function of each player is submodular and has antitone
Nash_equilibrium_computation
Award for advancements in discrete mathematics
Lisa Fleischer, Satoru Fujishige, and Alexander Schrijver for showing submodular minimization to be strongly polynomial. 2006: Manindra Agrawal, Neeraj
Fulkerson_Prize
Weighted tree representing s-t cuts of a graph
{\displaystyle (\{u\},\{v\})\in E_{T}} by (u, v). Output T. Using the submodular property of the capacity function c, one has c ( X ) + c ( Y ) ≥ c ( X
Gomory–Hu_tree
British mathematician (born 1945)
integer programming, submodular optimization, the group-theoretic approach and polyhedral analysis of fixed-charge network flow and production planning
Laurence_Wolsey
Integer matrices with +1 or −1 determinant; invertible over the integers. GL_n(Z)
223–246 Fujishige, Satoru (1984), "A System of Linear inequalities with a Submodular Function on (0, ±1) Vectors", Linear Algebra and Its Applications, 63:
Unimodular_matrix
Class of statistical modeling methods
only contains pair-wise potentials and the energy is submodular, combinatorial min cut/max flow algorithms yield exact solutions. If exact inference is
Conditional_random_field
MR 4915164 Edmonds, Jack; Giles, Rick (1977), "A min-max relation for submodular functions on graphs", Studies in integer programming (Proc. Workshop,
Woodall's_conjecture
Abstraction of linear independence of vectors
{\displaystyle r(A\cup B)+r(A\cap B)\leq r(A)+r(B)} . That is, the rank is a submodular function. (R4) For any set A {\displaystyle A} and element x {\displaystyle
Matroid
Vertex partition in a directed graph
MR 0499529 Edmonds, Jack; Giles, Rick (1977), "A min-max relation for submodular functions on graphs", Studies in integer programming (Proc. Workshop,
Dicut
American mathematician (1924–2021)
paper on this topic "On greedy algorithms, partially ordered sets and submodular functions," co-authored with Dietrich, appeared in 2003. Hoffman visited
Alan_J._Hoffman
SUBMODULAR FLOW
SUBMODULAR FLOW
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : occupational name denoting a servant who carried the ewer to guests at table so that they could wash their hands, Anglo-Norman French and Middle English ewerer (related to ewere ‘jug’), with the French definite article l’.Cornish : variant of Flower 4.
Boy/Male
Tamil
Flower, Blossom
Surname or Lastname
English
English : probably a habitational name from ‘The Leen’ (earlier Leon, ‘at the streams’) in Hereford or the Leen river in Nottinghamshire. Both are derived from a Celtic root verb lei- ‘flow’ (for example as in Welsh lliant ‘stream’).English : variant spelling of Lean.
Boy/Male
Tamil
Flower, Blossom
Surname or Lastname
English and French
English and French : from the personal name Florence, used by both sexes (Latin Florentius (masculine) and Florentia (feminine), ultimately from flos, genitive floris ‘flower’). Both names were borne by several early Christian martyrs, but in the Middle Ages the masculine name was far more common.English and French : local name for someone from Florence in Italy, originally named in Latin as Florentia.
Girl/Female
Tamil
A flower
Female
English
English name derived from the vocabulary word, "flower," from Proto-Indo-European *bhlo-, FLOWER means "to blossom, flourish."
Boy/Male
Indian, Sikh
Flowers
Surname or Lastname
English
English : from Anglo-Norman French gardinier ‘gardener’. In medieval times this normally denoted a cultivator of edible produce in an orchard or kitchen garden, rather than one who tended ornamental lawns and flower beds.Americanized form of French Desjardins or German Gärtner (see Gartner).
Boy/Male
Tamil
Flowering
Girl/Female
Australian, Christian, French, Latin, Portuguese
Blooming; Flower; Form of Florence
Surname or Lastname
English
English : habitational name from Lashbrook in Oxfordshire, named in Old English as ‘boggy stream’, from læcc ‘stream flowing through boggy land’, ‘bog’ + brÅc ‘brook’, ‘stream’ (with a more ancient meaning of ‘marsh’).
Surname or Lastname
English
English : nickname from Middle English flo(u)r ‘flower’, ‘blossom’ (Old French flur, from Latin flos, genitive floris). This was a conventional term of endearment in medieval romantic poetry, and as early as the 13th century it is also regularly found as a female personal name.English : metonymic occupational name for a miller or flour merchant, or perhaps a nickname for a pasty-faced person, from Middle English flo(u)r ‘flour’. This is in origin the same word as in 1, with the transferred sense ‘flower, pick of the meal’. Although the two words are now felt to be accidental homophones, they were not distinguished in spelling before the 18th century.English : occupational name for an arrowsmith, from an agent derivative of Middle English flŠ‘arrow’ (Old English flÄ).Welsh : Anglicized form of the Welsh personal name Llywarch, of unexplained origin.Translation of French Lafleur.
Surname or Lastname
English
English : variant spelling of Ling 1.Norwegian : habitational name from any of several farmsteads in western Norway named with lyng ‘heather’, either on its own, or with the addition of vin ‘meadow’.Dutch (de Linge) and North German : habitational name from a place named with Old Low German linge ‘strip of land or water’, or possibly with the river name Linge (this river flows through the Betuwe). See also Lingen.Possibly French, from a metonymic occupational name from linge ‘linen goods’, but there is no evidence of surname in North America.
Surname or Lastname
English
English : habitational name from Melhuish in Devon, so called from Old English mǣl(e) ‘brightly colored’, ‘flowery’ + hīwisc ‘hide’ (a measurement of land).Scottish : variant of Mellis 2.
Surname or Lastname
English
English : unexplained; possibly a variant of Flew, a metonymic occupational name for a fisherman, from Middle English flue, denoting a kind of fishing net.
Surname or Lastname
English
English : patronymic from Flower 1.
Girl/Female
French English
Flower.
Surname or Lastname
English
English : see Flow.
Surname or Lastname
English
English : topographic name for someone who lived by a small stream or an intermittent spring (Old English flÅd(e), from flÅwan ‘to flow’).Anglicized form of the Welsh personal name Llwyd (see Lloyd).Irish : translation of various names correctly or erroneously associated with Gaelic tuile ‘flood’ (see Toole).
SUBMODULAR FLOW
SUBMODULAR FLOW
Boy/Male
Indian
Kind hearted
Girl/Female
Arabic, Muslim
Name of Prophet Mohammed's Wife
Girl/Female
Muslim
Original
Girl/Female
Biblical
Pelican of God.
Girl/Female
Gujarati, Indian, Kannada
Beautiful Light; Divine Light
Girl/Female
Hindu, Indian
Pure; Clean; Happy
Girl/Female
Greek
Pure.
Boy/Male
Indian
Good Hearted
Boy/Male
Indian
Pureness, Pure, Precious
Female
Norwegian
Norwegian form of Old Norse ValdÃs, WALDIS means "goddess of the slain in battle."
SUBMODULAR FLOW
SUBMODULAR FLOW
SUBMODULAR FLOW
SUBMODULAR FLOW
SUBMODULAR FLOW
a.
Situated under, or at the bases of, the lobules of the liver.
n.
A tropical leguminous bush (Poinciana, / Caesalpinia, pulcherrima) with prickly branches, and showy yellow or red flowers; -- so named from its having been sometimes used for hedges in the West Indies.
a.
Having conspicuous flowers; -- used as an epithet with many names of plants; as, flowering ash; flowering dogwood; flowering almond, etc.
a.
Bearing three flowers together, or only three flowers.
adv.
In a flowing manner.
a.
Turgid; extravagant; bombastic; inflated; as, high-flown language.
a.
That flows or for flowing (in various sense of the verb); gliding along smoothly; copious.
a.
Abounding with flowers.
a.
Situated under, or on the ventral side of, the eye.
n.
The act of adorning with flowers.
n.
The goat's beard, whose flowers close at midday.
a.
Having no flowers.
n.
State of being without flowers.
n.
Flowing tendency or quality; fluency.
a.
Full of flowers; abounding with blossoms.
a.
Dressed with garlands of flowers.
a.
Highly embellished with figurative language; florid; as, a flowery style.
n.
The state of being flowery.