相关论文: A solution to a Partitioned Balanced Tournament De…

We construct a partitioned balanced tournament design of side nine.

E. R. Lamken prove in [5] that there exists a partitioned balanced tournament design of side $n$, PBTD($n$), for $n$ a positive integer, $n \ge 5$, except possibly for $n \in \{9,11,15\}$. In this article, we show the existence of PBTD($n$)…

A generalized balanced tournament design, or a GBTD(k, m) in short, is a (km, k, k-1)-BIBD defined on a km-set V . Its blocks can be arranged into an m\times(km-1) array in such a way that (1) every element of V is contained in exactly one…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

In some domestic professional sports leagues, the home stadiums are located in cities connected by a common train line running in one direction. For these instances, we can incorporate this geographical information to determine optimal or…

We describe a class of combinatorial design problems which typically occur in professional sailing league competitions. We discuss connections to resolvable block designs and equitable coverings and to scheduling problems in operations…

The bipartite traveling tournament problem (BTTP) addresses inter-league sports scheduling, which aims to design a feasible bipartite tournament between two $n$-team leagues under some constraints such that the total traveling distance of…

Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…

The obvious way to construct a GDD (group-divisible design) recursively is to use Wilson's Fundamental Construction for GDDs (WFC). Then a PBD (pairwise balanced design) is often obtained by adding a new point to each group of the GDD.…

A tournament is an oriented complete graph. The problem of ranking tournaments was firstly investigated by P. Erd\H{o}s and J. W. Moon. By probabilistic methods, the existence of "unrankable" tournaments was proved. On the other hand, they…

Given a set of numbers, the balanced partioning problem is to divide them into two subsets, so that the sum of the numbers in each subset are as nearly equal as possible, subject to the constraint that the cardinalities of the subsets be…

We consider a generalization of the notion of partially balanced incomplete block designs (PBIBDs), by relaxing the requirement that the underlying association scheme be commutative. An infinite family of such generalizations is…

Resolvable combinatorial designs including Resolvable Balanced Incomplete Block Designs, Resolvable Group Divisible Designs, Uniformly Resolvable Designs and Mutually Orthogonal Latin Squares and Rectangles are used to construct optimal…

The Traveling Tournament Problem(TTP) is a combinatorial optimization problem where we have to give a scheduling algorithm which minimizes the total distance traveled by all the participating teams of a double round-robin tournament…

In this work a balanced k-way partitioning problem with weight constraints is defined to model the sports team realignment. Sports teams must be partitioned into a fixed number of groups according to some regulations, where the total…

We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In…

We show that computing an equilibrium in atomic splittable congestion games with player-specific affine cost functions $l_{e,i}(x) = a_{e,i} x + b_{e,i}$ is $\mathsf{PPAD}$-complete. To prove that the problem is contained in…

Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the…

In this paper, we consider the computational protein design (CPD) problem, which is usually modeled as a 0/1 programming and is extremely challenging due to its combinatorial properties. We propose an efficient algorithm for solving it.…

This paper proposes an asymmetric perturbation technique for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Perturbing payoffs or values is known to be…