SIAM Digital Library
 
 
 

SIAM J. on Discrete Mathematics

BROWSE VOLUMES

Year Range: 

All Journal content published prior to 1997 is part of LOCUS.

Search Issue | RSS Feeds RSS
Previous Issue

1988

Volume 1, Issue 4 (partial)


On the Influence of Single Participant in Coin Flipping Schemes

Benny Chor and Mihály Geréb-Graus

SIAM J. Discrete Math. 1, pp. 411-415 (5 pages) | Cited 1 time

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
This paper proves that in a one-round fair coin flipping scheme with $n$ participants, either the average influence of all participants is at least $3/n - o( 1/n )$, or there is at least one participant whose influence is $\Omega ( n^{ - 5 /6} )$.

Matroids and Subset Interconnection Design

Ding-Zhu Du and Zevi Miller

SIAM J. Discrete Math. 1, pp. 416-424 (9 pages) | Cited 3 times

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
A problem arising in the design of vacuum systems and having applications to some natural problems of interconnection design is described as follows.(1) Given a set $X$ and subsets $X_i ,Y_i $ of $X,i = 1, \cdots ,n$, satisfying $X_i \cap Y_i = \O $, find a graph $G$ with vertex set $X$ and the minimum number of edges such that for any $i$, the subgraph induced by $X\backslash Y_i $ has a connected component containing $X_i $.
Two other problems related to this one are the following ones. (2) Given a set $X$ and subsets $X_1 ,X_2 , \cdots ,X_n $ such that $X = \cup _{i = 1}^n X_i $, find a graph $G$ with vertex set $X$ and the minimum number of edges such that for any $i$ the subgraph $G_i $ induced by $X_i $ in $G$ is connected. (3) Given a set $X$ and subsets $X_1 ,X_2 , \cdots ,X_n $ such that $X = \cup _{i = 1}^n X_i $, find a graph $G$ with vertex set $X$, find a graph $G$ with vertex set $X$ and the minimum number of edges such that for any subset $I$ of $\{ 1, \cdots ,n \}$, the subgraph induced by $ \cap _{i \in I} X_i $ is connected.
This paper shows that (3) is polynomial-time solvable while (1) and (2) are NP-complete. Also, some heuristics for (1) and (2) are given. The solution of (3) is an interesting application of matroid theory.

Laguerre Polynomials, Weighted Derangements, and Positivity

Dominique Foata and Doron Zeilberger

SIAM J. Discrete Math. 1, pp. 425-433 (9 pages) | Cited 9 times

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
A calculation of the linearization coefficients of the (generalized) Laguerre polynomials $L_n^{( \alpha )} ( x )$ is proposed by means of analytic and combinatorial methods. This paper extends to the case of an arbitrary $\alpha $ a combinatoric and analytic result due to Askey, Ismail, and Koornwinder and Even and Gillis.

Parallel Symmetry-Breaking in Sparse Graphs

Andrew V. Goldberg, Serge A. Plotkin, and Gregory E. Shannon

SIAM J. Discrete Math. 1, pp. 434-446 (13 pages) | Cited 18 times

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
This paper describes efficient deterministic techniques for breaking symmetry in parallel. These techniques work well on rooted trees and graphs of constant degree or genus. The primary technique allows us to 3-color a rooted tree in $O( \lg^* n )$ time on an EREW PRAM using a linear number of processors. These techniques are used to construct fast linear processor algorithms for several problems, including the problem of $( \Delta + 1)$-coloring constant-degree graphs and 5-coloring planar graphs. Lower bounds for 2-coloring directed lists and for finding maximal independent sets in arbitrary graphs are also proved.

Recognizing Bellman–Ford-Orderable Graphs

Ramsey W. Haddad and Alejandro A. Schäffer

SIAM J. Discrete Math. 1, pp. 447-471 (25 pages)

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
Mehlhorn and Schmidt [Discrete Appl. Math., 15 (1986), pp. 315–327 ] consider the following problem. Given a directed graph with distinguished source vertex $s$, is it possible to order the edges so that all simple paths starting at $s$ use edges in increasing order? They show how to solve their problem in $O( | E |^2 )$ steps, where $| E |$ is the number of edges. An algorithm that runs in $O( | V |^2 )$ steps is given, where $| V |$ is the number of vertices. The new algorithm and its analysis apply and extend previous results on dominators in directed graphs.

On Restricted Two-Factors

Pavol Hell, David Kirkpatrick, Jan Kratochvíl, and Igor Kříž

SIAM J. Discrete Math. 1, pp. 472-484 (13 pages) | Cited 6 times

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
A two-factor of $G$ consists of disjoint cycles that cover $V( G )$. The authors consider the existence problem for two-factors in which the cycles are restricted to having lengths from a prescribed (possibly infinite) set of integers. Theorems are presented which derive the existence of such restricted two-factors in $G$ from their existence in $G - u$ and $G - v $. The possibility of such theorems is then related to the complexity of the corresponding existence problem. In particular, the only four cases in which polynomial algorithms can be expected (in the sense that all other cases are shown to be NP-hard) are identified.

Silverman Games on Disjoint Discrete Sets

G. A. Heuer and W. Dow Rieder

SIAM J. Discrete Math. 1, pp. 485-525 (41 pages) | Cited 2 times

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
Previous work by Heuer on Silverman games on odd versus even positive integers with threshold $T > 1$ and penalty $\nu > 0$, is extended to games on more general strategy sets $S_1 $ and $S_2 $ of positive numbers. Much of this paper is devoted to games where $S_1 $ and $S_2 $ are disjoint and discrete. Results include complete classification and solutions for $T\leqq T^* $ (where $T^*$ depends on $S_1$ and $S_2$), complete classification and solutions for $T > T^* $ and $\nu \geqq 1$, and partial classification with solutions for $T > T^ * $ and $\nu < 1$.

The Linearity of First-Fit Coloring of Interval Graphs

H. A. Kierstead

SIAM J. Discrete Math. 1, pp. 526-530 (5 pages) | Cited 16 times

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
It is shown that First-Fit coloring requires at most $40\omega $ colors to color an interval graph with clique size $\omega $. It follows that a polynomial time approximation algorithm for Dynamic Storage Allocation due to Chrobak and Slusarek has a constant performance ratio of 80.

Broadcast Networks of Bounded Degree

Arthur L. Liestman and Joseph G. Peters

SIAM J. Discrete Math. 1, pp. 531-540 (10 pages) | Cited 8 times

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. Several previous papers have investigated ways to construct sparse graphs (networks) in which this process can be completed in minimum time from any originator. The graphs produced by these methods contain high degree vertices. This paper describes graphs with fixed maximum degree in which broadcasting can be completed in near minimum time.

Distribution of the Symmetric Difference Metric on Phylogenetic Trees

M. A. Steel

SIAM J. Discrete Math. 1, pp. 541-551 (11 pages) | Cited 5 times

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
The symmetric difference metric has been useful in comparing phylogenetic trees derived from DNA sequence data. The main result shown here is that the frequency of pairs of binary trees a given distance apart is described by a limiting Poisson distribution, with $e^{ -1 / 8} \approx 88$ percent of all pairs maximally distant. Asymptotic bounds on the distribution are derived, and the asymptotic mean and variance of the normalized metric on the class of all phylogenetic trees is also calculated. The results rely on simple combinatorial constructions and analytic properties of appropriate generating functions.

The Complexity of Metric Realization

Peter Winkler

SIAM J. Discrete Math. 1, pp. 552-559 (8 pages) | Cited 6 times

Online Publication Date: August 08, 2006

Full Text: | Download PDF

Show Abstract
It is shown that the problem of realizing a metric by a graph or network with minimum total edge-length is, depending on the version, NP-hard or NP-complete.
In particular, Discrete Metric Realization (DMR) is NP-complete “in the strong sense,” where DMR is defined as follows:
INSTANCE. An $n$-by-$n$ integer-entry distance matrix $D = ( d_{i,j} )$ and a positive integer $k$;
QUESTION. Is there a graph $G = \langle V,E \rangle $ with distinguished vertices $v _1 ,v _2 , \cdots ,v _n $ that realize $D$, i.e., the number of edges in a shortest path between $v _i $ and $v _j $ is exactly $d_{i,j} $ for each $1\leqq i\leqq j\leqq n$, and such that the total number of edges of $G$ is at most $k$?
Close

Your Recent History Recent History Help

Recently Viewed

  1. Mean Field Games: Numerical Methods for the Planning Problem
  2. A Convex Condition for Robust Stability Analysis via Polyhedral Lyapunov Functions
  3. Stability and Resolution Analysis for a Topological Derivative Based Imaging Functional
  4. Experimental Design for Biological Systems
  5. Linear Programming and Constrained Average Optimality for General Continuous-Time Markov Decision Pr...
© SIAM By using SIAM Publications Online you agree to abide by the Terms and Conditions of Use. Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Bristol, UK).
close