Non-evasiveness is a further strengthening of collapsibility, emerged in theoretical computer science and later studied by Kahn, Saks and Sturtevant [9] and Welker [11]. A 0-dimensional complex is non-evasive if and only if it consists of a single point. Recursively, a d-dimensional simplicial complex (d > 0) is non-evasive if and only if there is some vertex v whose link and deletion are both ...

Let h > w > 0 be two fixed integers. Let H be a random hypergraph whose hyperedges are all of cardinality h. To w-orient a hyperedge, we assign exactly w of its vertices positive signs with respect to the hyperedge, and the rest negative. A (w, k)-orientation of H consists of a w-orientation of all hyperedges of H, such that each vertex receives at most k positive signs from its incident hypere...

We investigate a linear time greedy algorithm for the following load balancing problem: Assign m balls to n bins such that the maximum occupancy is minimized. Each ball can be placed into one of two randomly choosen bins. This problem is closely related to the problem of orienting the edges of an undirected graph to obtain a directed graph with minimum in-degree. Using differential equation met...

For a graph G, let t(G) denote the maximum number of vertices in an induced subgraph of G that is a tree. In this paper, we study the problem of bounding t(G) for graphs which do not contain a complete graph Kr on r vertices. This problem was posed twenty years ago by Erdős, Saks, and Sós. Substantially improving earlier results of various researchers, we prove that every connected triangle-fre...

Trying to construct a definition that covers a large heterogeneous group of complementary and alternative therapies is difficult. Many therapies are well known whereas others may be exotic, mysterious or even dangerous. Some relaxation techniques, massage therapies, special diets and self-help groups could be considered to be lifestyle choices rather than true therapeutic interventions, althoug...

We consider nondeterministic D-way branching programs computing functions f : D → {0, 1} in time at most kn. In the boolean case, where D = {0, 1}, no exponential lower bounds are known even for k = 2. Ajtai has proved such lower bounds for explicit functions over domains D of size at least n, and Beame, Saks and Thathachar for explicit functions over domains of size at least 2 k . In this note...

The cut number S(d) of the d-cube is the minimum number of hyperplanes in R that slice, that is cut the edges while avoiding vertices, all the edges of the d-cube. The cut number problem for the hypercube of dimensions d ≥ 4 was posed by P. O’Neil more than thirty years ago [17]. The identity S(3) = 3 is easy and that of S(4) = 4 is a well-known result, see [5,6,18]. However, the conjecture of ...

The currently fastest known algorithm for k-SAT is PPSZ named after its inventors Paturi, Pudlák, Saks, and Zane [7]. Analyzing its running time is much easier for input formulas with a unique satisfying assignment. In this paper, we achieve three goals. First, we simplify Hertli’s 2011 analysis [1] for input formulas with multiple satisfying assignments. Second, we show a “translation result”:...

right of private property is of the most important individual rights of society that lies in the heart of private law. in islamic law protection of property as one of the five goals of fighhe, that is, protection of sagacity, religion, generation and self, is to be stipulated. based on article 140 of civil code the process of property acquisition is restricted to four cases. on the other hand, ...

We introduce new models for dynamic computation based on the cell probe model of Fredman and Yao. We give these models access to nondeterministic queries or the right answer ±1 as an oracle. We prove that for the dynamic partial sum problem, these new powers do not help, the problem retains its lower bound of Ω(log n/ log log n). From these results we easily derive a large number of lower bound...