Results 1  10
of
31
Pruning by Isomorphism in BranchandCut
, 2001
"... The paper presents a BranchandCut for solving (0, 1) integer linear programs having a large symmetry group. The group is used for pruning the enumeration tree and for generating cuts. The cuts are non standard, cutting integer feasible solutions but leaving unchanged the optimal value of the probl ..."
Abstract

Cited by 30 (1 self)
 Add to MetaCart
The paper presents a BranchandCut for solving (0, 1) integer linear programs having a large symmetry group. The group is used for pruning the enumeration tree and for generating cuts. The cuts are non standard, cutting integer feasible solutions but leaving unchanged the optimal value of the problem. Pruning and cut generation are performed by backtracking procedures using a SchreierSims table for representing the group. Applications to the generation of covering designs and error correcting codes are presented.
Exploiting orbits in symmetric ilp
 Mathematical Programming
"... This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an authorized administrator of Research Showcase. For more information, please contact kbehrman@andrew.cmu.edu. Mathematical Programming manuscript No. (wi ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an authorized administrator of Research Showcase. For more information, please contact kbehrman@andrew.cmu.edu. Mathematical Programming manuscript No. (will be inserted by the editor)
The Steiner Triple Systems of Order 19
 Math. Comp
"... Using an orderly algorithm, the Steiner triple systems of order 19 are classified; there are 11,084,874,829 pairwise nonisomorphic such designs. For each design, the order of its... ..."
Abstract

Cited by 17 (6 self)
 Add to MetaCart
Using an orderly algorithm, the Steiner triple systems of order 19 are classified; there are 11,084,874,829 pairwise nonisomorphic such designs. For each design, the order of its...
Searching for Macro Operators with Automatically Generated Heuristics
"... . Macro search is used to derive solutions quickly for large search spaces at the expense of optimality. We present a novel way of building macro tables. Our contribution is twofold: (1) for the first time, we use automatically generated heuristics to find optimal macros, (2) due to the speedup ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
. Macro search is used to derive solutions quickly for large search spaces at the expense of optimality. We present a novel way of building macro tables. Our contribution is twofold: (1) for the first time, we use automatically generated heuristics to find optimal macros, (2) due to the speedup achieved by (1), we merge consecutive subgoals to reduce the solution lengths. We use the Rubik's Cube to demonstrate our techniques. For this puzzle, a 44% improvement of the average solution length was achieved over macro tables built with previous techniques. 1
Algorithms for Matrix Groups and the Tits Alternative
 Proc. 36th IEEE FOCS
, 1999
"... l over the generators grows as c l for some constant c>1 depending on G. For groups with abelian subgroups of finite index, we obtain a Las Vegas algorithm for several basic computational tasks, including membership testing and computing a presentation. This generalizes recent work of Beals an ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
l over the generators grows as c l for some constant c>1 depending on G. For groups with abelian subgroups of finite index, we obtain a Las Vegas algorithm for several basic computational tasks, including membership testing and computing a presentation. This generalizes recent work of Beals and Babai, who give a Las Vegas algorithm for the case of finite groups, as well as recent work of Babai, Beals, Cai, Ivanyos, and Luks, who give a deterministic algorithm for the case of abelian groups. # 1999 Academic Press Article ID jcss.1998.1614, available online at http:##www.idealibrary.com on 260 00220000#99 #30.00 Copyright # 1999 by Academic Press All rights of reproduction in any form reserved. * Research conducted while visiting IAS and DIMACS and supported in part by an NSF Mathematical Sciences
Errorcorrecting codes from permutation groups
 Discrete Math
"... We replace the usual setting for errorcorrecting codes (i.e. vector spaces over finite fields) with that of permutation groups. We give an algorithm which uses a combinatorial structure which we call an uncoveringbybases, related to covering designs, and construct some examples of these. We also ..."
Abstract

Cited by 10 (9 self)
 Add to MetaCart
We replace the usual setting for errorcorrecting codes (i.e. vector spaces over finite fields) with that of permutation groups. We give an algorithm which uses a combinatorial structure which we call an uncoveringbybases, related to covering designs, and construct some examples of these. We also analyse the complexity of the algorithm. We then formulate a conjecture about uncoveringsbybases, for which we give some supporting evidence and prove for some special cases. In particular, we consider the case of the symmetric group in its action on 2subsets, where we make use of the theory of graph decompositions. Finally, we discuss the implications this conjecture has for the complexity of the decoding algorithm.
Binary Linear Codes: New Results on Nonexistence
, 1996
"... ly, a constraint is a relation of the form a 1 v 1 + · · · +a n v n k, where v 1 , . . . , v n are variables, a 1 , . . . , a n # Q , k # Z, and is either #, #, or =. Constraints are represented in several different ways, according to what variables and coefficients are allowed: 1. Whe ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
ly, a constraint is a relation of the form a 1 v 1 + · · · +a n v n k, where v 1 , . . . , v n are variables, a 1 , . . . , a n # Q , k # Z, and is either #, #, or =. Constraints are represented in several different ways, according to what variables and coefficients are allowed: 1. When constraints appear in commands, the variables are arbitrary (within the confines of the language), and the coefficients are in Z. 2. These constraints are internally represented (using the "constraint" class) in the same way, except that Q coefficients are allowed. This is because some internal operations may result in constraints whose coefficients are not integers. (This can happen when the "incorporate" command is used.) 3. For split linear programming calculations, constraints are first converted to constraints involving v variables and having coefficients in Q (class qvconstraint). 4. Clearing denominators yields constraints having v variables and coefficients in Z (class vconstra...
Computing in groups of Lie type
 Math. Comp
, 2001
"... Abstract. We describe two methods for computing with the elements of untwisted groups of Lie type: using the Steinberg presentation and using highest weight representations. We give algorithms for element arithmetic within the Steinberg presentation. Conversion between this presentation and linear r ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
Abstract. We describe two methods for computing with the elements of untwisted groups of Lie type: using the Steinberg presentation and using highest weight representations. We give algorithms for element arithmetic within the Steinberg presentation. Conversion between this presentation and linear representations is achieved using a new generalisation of row and column reduction. 1.
A new existence proof of Janko’s simple group J4
 In Computational Methods for Representations of Groups and Algebras, volume 173 of Progress in Mathematics
, 1999
"... Janko’s large simple sporadic group J4 was originally constructed by Benson, ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
Janko’s large simple sporadic group J4 was originally constructed by Benson,
Symmetric ILP: coloring and small integers
 Discrete Optimization
"... This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an