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We present new pivot rules for the Simplex method for LPs over 0/1 polytopes. We show that the number of non-degenerate steps taken using these rules is strongly polynomial and even linear in the dimension or in the number of variables. Our…

Optimization and Control · Mathematics 2021-11-30 Alexander Black , Jesús De Loera , Sean Kafer , Laura Sanità

We investigate the iterative behaviour of continuous order preserving subhomogeneous maps that map a polyhedral cone into itself. For these maps we show that every bounded orbit converges to a periodic orbit and, moreover, that there exists…

Dynamical Systems · Mathematics 2007-05-23 Marianne Akian , Stephane Gaubert , Bas Lemmens , Roger Nussbaum

A discrete temporal constraint satisfaction problem is a constraint satisfaction problem (CSP) whose constraint language consists of relations that are first-order definable over $(\Bbb Z,<)$. Our main result says that every distance CSP is…

Logic · Mathematics 2016-04-27 Manuel Bodirsky , Barnaby Martin , Antoine Mottet

We call a continuous path of polygons decreasing if the convex hulls of the polygons form a decreasing family of sets. For an arbitrary polygon of more than three vertices, we characterize the polygons contained in it that can be reached by…

Metric Geometry · Mathematics 2025-06-09 Isaac Kulp , Charlotte Ochanine , Logan Richard , Leonel Robert , Scott Whitman

We write exact equations for the thermodynamic properties of a linear polymer molecule confined to walk on a lattice of finite size. The dimension of the space in which the lattice resides can be arbitrary. We also calculate polymer…

General Physics · Physics 2011-10-04 Esdmund A. Di Marzio , Charles M. Guttman

We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our…

Optimization and Control · Mathematics 2012-01-17 Thomas L. Magnanti , Dan Stratila

Speedup measures how much faster we can solve the same problem using many cores. If we can afford to keep the execution time fixed, then quality up measures how much better the solution will be computed using many cores. In this paper we…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-09-06 Jan Verschelde , Genady Yoffe

We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix $M\in{\mathbb R}^{n\times n}$ can be decomposed as $M=\Phi U +…

Machine Learning · Computer Science 2013-01-01 Geoffrey J. Gordon

The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly…

Statistical Mechanics · Physics 2024-03-05 Yuki Ishiguro , Jun Sato

The polytope containment problem is deciding whether a polytope is a contained within another polytope. This problem is rooted in computational convexity, and arises in applications such as verification and control of dynamical systems. The…

Optimization and Control · Mathematics 2019-03-14 Sadra Sadraddini , Russ Tedrake

The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb C$ is introduced; it contains the class $\mathcal P$ of polynomial time problems over $\mathbb C$. The $\tau$-Conjecture for polynomials implies that…

Numerical Analysis · Mathematics 2025-10-20 Gregorio Malajovich

The Canadian traveler problem (CTP) is the problem of traversing a given graph, where some of the edges may be blocked - a state which is revealed only upon reaching an incident vertex. Originally stated by Papadimitriou and Yannakakis…

Computational Complexity · Computer Science 2012-07-20 Dror Fried , Solomon Eyal Shimony , Amit Benbassat , Cenny Wenner

We study the last passage time in geometric last passage percolation (LPP). As the system size increases, we derive precise large deviation probabilities -- up to and including the constant terms -- for both the lower and upper tails. A key…

Probability · Mathematics 2025-10-21 Sung-Soo Byun , Christophe Charlier , Philippe Moreillon , Nick Simm

The rate of escape of polymers from a two-dimensionally confining potential well has been evaluated using self-avoiding as well as ideal chain representations of varying length, up to 80 beads. Long timescale Langevin trajectories were…

Soft Condensed Matter · Physics 2015-03-27 Harri Mökkönen , Timo Ikonen , Tapio Ala-Nissila , Hannes Jónsson

We give estimates for the probability that a chordal, radial or two-sided radial SLE$_\kappa$ curve retreats far from its terminal point after coming close to it, for $\kappa \leq 4$. The estimates are uniform over all initial segments of…

Probability · Mathematics 2015-02-13 Laurence S. Field , Gregory F. Lawler

For systems of polynomial equations, we study the problem of computing the Newton polytope of their eliminants. As was shown by Esterov and Khovanskii, such Newton polytopes are mixed fiber polytopes of the Newton polytopes of the input…

Symbolic Computation · Computer Science 2025-03-17 Rafael Mohr , Yulia Mukhina

This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are…

Optimization and Control · Mathematics 2019-10-25 Feng Guo , Xiaoxia Sun

The Symmetric Exclusion Process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of…

Statistical Mechanics · Physics 2018-06-13 Alexis Poncet , Olivier Bénichou , Vincent Démery , Gleb Oshanin

We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…

Data Structures and Algorithms · Computer Science 2023-12-08 David Gamarnik , Devin Smedira

Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set is discrete and is given explicitly. We propose new…

Computational Geometry · Computer Science 2025-04-24 Jean Cardinal , Xavier Goaoc , Sarah Wajsbrot